Curriculum Vitae
(incl. lists of
publications, presentations, and students)
Mogens Steffensen
Education:
- 2001, Ph.D. in Actuarial
Mathematics, University of Copenhagen
- 1997, Cand.Act.
(M.Sc. in Actuarial Mathematics), University of Copenhagen
- 1995, B.Sc. in Actuarial
Mathematics, University of Copenhagen
- 1989, General Certificate of
Education, Vejen Gymnasium
Positions
and longer visits (part-time and full-time):
- 2008- , Professor
(with special duties) in life insurance mathematics, Uni. Of Cph.
- 2005, Visitor at Department of
Statistics, London School of Economics and Political Science, UK
- 2004-2008, Associate Professor,
Laboratory of Act. Math., Uni. of Cph.
- 2003, Visitor
at Arbeitsgruppe Stochastische Steuerung und
Finanzmathematik, Uni. of Kaiserslautern,
Germany
- 2001-2004, Assistant Professor,
Laboratory of Act. Math. Univ. of Cph.
- 2000, Visitor at Department of
Applied Mathematics and Statistics, Stony Brook Uni., New York, USA
- 1999, Visitor
at Lehrstuhl für Versicherungswissenschaft, Uni.
of Karlsruhe, Germany
- 1998-2001, Ph.D. student,
Laboratory of Act. Math., Uni. of Cph.
- 1997-1998, Research Assistant,
Laboratory of Act. Math., Uni. of Cph.
- 1995-1996, Tutor in Life
Insurance Mathematics, Laboratory of Act. Math.,
Uni. of Copenhagen.
- 1993-1997, Assistant in Danica (Danish life insurance company)
Professional:
- 2011-. Project manager at Actulus: Actuarial Calculus and Computing. Supported
by The Danish National Advanced Technology Foundation (Højteknologifonden).
- 2011-. Research Area Manager at
the research center HIPERFIT: Functional High-Performance
Computing for Financial Information Technology. Supported
by The Strategic Research Council
(Det strategiske forskningsråd)
- 2009-. Member of the network
Danish Center for Accounting and Finance. Supported by Nykredit A/S.
- 2009-. Head of the research
group Mathematical and Statistical Methods in Insurance and Economics,
Department of Mathematical Sciences, Uni. of Copenhagen.
- 2007-. Member of the Accounting
Committee under the Danish Actuarial Association.
- 2006-. Editor of Scandinavian
Actuarial Journal.
- 2006-2009. Member of the
network Danish Center for Accounting and
Finance. Supported by FSE
(Forskningsrådet for Samfund og Erhverv) and Nykredit A/S.
- 2005-2007. Member of the
network Multivariate Risk Models for Finance and Insurance. Supported by
FNU (Forskningsrådet for Natur
og Univers).
- 2004-2005. Member of the
network Mathematical Finance Network.. Supported by SSF (Statens Samfundsvidenskabelige
Forskningsråd).
- 2003-2007. Member of the
Continued Professional Development Committee under the Danish Actuarial
Association (Chairman 2005-2006).
- 2002-2004. Member of the
network Stochastic Models for Risk and Extremes. Supported by SNF (Statens Naturvidenskabelige Forskningsråd).
- 1997-. Member of the Danish
Actuarial Association.
Refereed Publications:
- 2011. Consumption-Portfolio Optimization with
Recursive Utility in Incomplete Markets. To appear in Finance and Stochastics. (Jointly
with Holger Kraft and Frank Thomas Seifried)
- 2011. Optimal Consumption and
Investment under Time-Varying Relative Risk Aversion. Journal of Economic Dynamics and Control.
35(5): 659-667.
- 2011. Household Consumption, Investment
and Life Insurance. Insurance: Mathematics and Economics. 48(3): 315-325. (Jointly with Kenneth Bruhn)
- 2009. Asset Allocation with Contagion and
Explicit Bankruptcy Procedures. Journal of Mathematical Economics
45(1-2): 147-167. (Jointly with H. Kraft)
- 2009. A Two-Account Model for
Pension Saving Contracts. Scandinavian Actuarial Journal 2009(3): 169 – 186. (Jointly with S. Waldstrøm)
- 2008. The Policyholder’s Static
and Dynamic Decision Making of Life Insurance and Pension Payments. Blätter der
DGVFM 29(2):
211-244. (Jointly with H. Kraft)
- 2008. Optimal investment and
life insurance strategies under minimum and maximum constraints. Insurance:
Mathematics and Economics
43(1): 15-28. (Jointly with
P. H. Nielsen)
- 2008. Optimal Consumption and
Insurance: A Continuous-Time Markov Chain Approach. ASTIN
Bulletin 28(1):231-257. (Jointly with H. Kraft)
- 2008. How to Invest Optimally
in Corporate Bonds: A Reduced-Form Approach. Journal of Economic
Dynamics and Control 32(2):348-385. (Jointly with H. Kraft)
- 2007. On
Worst Case Portfolio Optimization. SIAM Journal on Control and
Optimization 46(6): 2013-2030. (Joint with
R. Korn)
- 2007. Bankruptcy, Counterparty
Risk, and Contagion. Review of Finance 2007; 11, 209-252. (Jointly
with H. Kraft)
- 2006. Quadratic Optimization of
Life Insurance Payment Streams. ASTIN Bulletin 36
(1):245-267.
- 2006. Surplus-linked Life
Insurance. Scandinavian Actuarial Journal, 2006(1):1-22.
- 2006. Portfolio Problems
Stopping at First Hitting Time with Applications to Default Risk. Mathematical
Methods of Operations Research, 63(1):123-150. (Jointly with H. Kraft)
- 2005. A Note on the Free Policy
Reserve. Blätter der
DGVFM, Band XXVII, Heft 2, Oktober 2005.
- 2005. What is the Time Value of
a Stream of Investments? Journal of Applied Probability, 42,
861-866. (Jointly with R. Norberg)
- 2004. On
Merton's Problem for Life Insurers. ASTIN Bulletin
34(1):5-25.
- 2002. Intervention Options in
Life Insurance. Insurance: Mathematics and Economics 31:71-85.
- 2000. A No Arbitrage Approach
to Thiele's Differential Equation. Insurance: Mathematics and Economics,
27: 201-214.
Working papers:
- 2012. Worst-Case-Optimal
Dynamic Reinsurance for Large Claims (March 25, 2012). Available at SSRN: http://ssrn.com/abstract=2032525.
(jointly with Ralf Korn and Olaf Menkens)
- 2011. A Dynamic Programming
Approach to Constrained Portfolios (December 7, 2011). Available at SSRN: http://ssrn.com/abstract=1969418.
(jointly with Holger Kraft)
- 2011. On the Theory of
Continuous-Time Recursive Utility (November 7, 2011). Available at SSRN: http://ssrn.com/abstract=1954655.
- 2011. Inconsistent Investment
and Consumption Problems (March 29, 2011). Available at SSRN: http://ssrn.com/abstract=1794174. (jointly with Morten
Tolver Kronborg)
- 2011. Safe-Side Scenarios for
Financial and Biometrical Risk (January 11, 2011). Available at SSRN: http://ssrn.com/abstract=1738552. (jointly with Marcus Christian
Christiansen)
- 2010. Some Solvable Portfolio
Problems with Quadratic and Collective Objectives (March 23, 2010).
Available at SSRN: http://ssrn.com/abstract=1577265. (jointly with Esben Masotti Kryger)
Books,
book articles, and miscellaneous:
1. 2011.
Sæt fokus på din udbetalingsprofil – en sammenligning af moderne
pensionsprodukter med markedsrente. Finans/Invest, september
– nr. 6 – 2011. (Jointly with Per Linnemann and
Kenneth Bruhn)
2. 2011. Functional High Performance Financial
IT - The HIPERFIT Research Center in Copenhagen. To appear in the proceedings
of ftp 2011 (12th International Symposium Trends in Functional Programming
2011). (Jointly with Jost Berthold, Ken Friis Larsen, Fritz Henglein, Andrzej Filinski, and Brian Vinter)
3. 2009. Life Insurance. In: Encyklopedia of Quantitative Finance.
4. 2008.
Liv og død på formel. Finans/Invest, juni – nr. 4 – 2008. (Jointly with Thomas Møller)
5. 2007. Market-Valuation Methods in
Life and Pension Insurance. Cambridge University Press. (Jointly with Thomas Møller)
6. 2007. CDOs in Chains. Working paper.
Willmott magazine, May 2007 – issue 29.
(Jointly with J. de Kock and H. Kraft)
7. 2007. Differential Equations in
Finance and Life Insurance. In: Jensen, B.S. and Palokangas,
T. (2007) Stochastic Economic Dynamics. CBS press.
8. 2001. On
Valuation and Control in Life and Pension Insurance. Ph.D. Thesis. Institute
for Mathematical Sciences, University of Copenhagen.
9.
2000.
Contingent Claims Analysis in Life and Pension Insurance. Proceedings 10th AFIR Colloquium
2000, 587-603.
Presentations
(Talks, lectures, and short courses):
- On Consistent Decision Making and the Theory
of Recursive Utility, Seminar, Köln, April 2012.
- On the Theory of Recursive Utility, Oberwolfach, January 2012.
- On the Theory of Recursive Utility,
Seminar, Copenhagen, December 2011.
- On the Theory of Recursive Utility,
Seminar, Torino, November 2011.
- On the Theory of Recursive Utility, Swissquote conference, Lausanne, October 2011.
- Quadratic and Collective Objectives,
Consistency, and Recursive Utility, Seminar, Maastrict,
September 2011.
- Credit Risk Modelling
and Management, European Actuarial Academy Seminar, Copenhagen, June 2011.
- Some Solvable Portfolios with Quadratic
and Collective Objectives, Seminar, Dublin, March 2011.
- Some Solvable Portfolios with Quadratic
and Collective Objectives, Seminar, Hannover, January 2011.
- Some Solvable Portfolios with Quadratic
and Collective Objectives, Seminar, Bergen, November 2010.
- Some Solvable Portfolios with Quadratic
and Collective Objectives, Seminar, Bonn, May 2010.
- Some Solvable Portfolios with Quadratic
and Collective Objectives, Seminar, København,
January 2010.
- Interviewundersøgelse om
Skandia Pension, Analyse og kommentarer, Skandia Invest Forum, København, December 2009.
- Livsforsikringsmatematisk
Essays. Den Danske Aktuarforening, København, December
2009.
- Pension fund management based on solutions
to constrained consumption-investment problems. Life Colloquium, Munich, September 2009.
- 50 ways to leave your stocks. Humboldt University, Berlin, July 2009.
- 50 ways to leave your stocks.
British-Nordic congress of Mathematicians , Oslo,
June 2009
- Pension fund management based on solutions
to constrained consumption-investment problems. CMA workshop on Insurance
mathematics and longevity risk, Oslo, May
2009.
- Constrained portfolio optimization with
applications to insurance. Cologne Life Insurance Day, Cologne,
March 2009.
- Det er koldt og man må gå
sig varm: Om finanskrise, kundernes valgmuligheder og Markovprocesser
i pensionsbranchen. Dansk Selskab for Teoretisk Statistik, København, December 2008.
- On optimal decision making in a life
insurance multi-state Markov model. Universität
Rostock, December 2008.
- On qualitative modelling and management of
insurable and securitizable risks. Center for Advanced Security Studies, Copenhagen 2008.
- Optimal Control in Finite State Markov
Chains with Applications to Personal Finance and Credit Risk Management. Workshop on Optimization and
Optimal Control. Linz, Austria, October
2008.
- Allocation with Contagion and Explicit
Bankruptcy Procedures. Symposium on Stochastic Dynamic Models in Finance
and Economics, Odense, August 2008.
- Moderne metoder
i livsforsikring. The
Danish Society of Actuaries, Copenhagen,
June 2008.
- What Has Finance Done for Life Insurance –
and vice versa. Oberwolfach,
February, 2008.
- What Has Finance Done for Life Insurance –
and vice versa. Workshop on Finance, Stochastics and Insurance, Bonn,
February 2008.
- Market-Valuation Methods in Life and
Pension Insurance. International Summer School, Swiss Association of
Actuaries. Scientific Director (with T. Møller),
Lausanne, August 2007.
- From Life Insurance to Credit Risk: On
Optimal Decisions in a Multi-state Model. Heriot-Watt University, Edingburgh, May 2007.
- Moderne metoder
i livsforsikring. The
Danish Society of Actuaries, Copenhagen,
April 2007.
- Market-Valuation Methods in Life and
Pension Insurance. Third Brazilian Conference on Statistical Modelling in
Insurance and Finance, Maresias, March 2007.
- Decisions and Design in Life and Pension
Insurance. Risk and Stochastics Day, London School of Economics and Political Science,
March 2007.
- From Life Insurance to Credit Risk: On
Portfolio Choice in Multistate Markov Chains. Danish Center for Accounting and Finance, Sandbjerg, March 2007.
- Decisions and Design in Life and Pension
Insurance. Oberwolfach, February 2007.
- Decisions and Design in Life and Pension
Insurance. Cass Business School, November
2006.
- Finansiering og forsikring:
Er det matematik? Ungdommens Naturvidenskabelige Forening, Copenhagen, September 2006.
- Optimal Consumption and Insurance. 21st
European Conference on Operations Research, Reykjavik, July 2006.
- Accounting for Intervention Options. 28th
International Congress of Actuaries, Paris, June 2006.
- How to Invest Optimally in Corporate
Bonds: A Reduced-Form Approach. Tanaka
Business School, Imperial College, London, UK, November 2005.
- How to Invest Optimally in Corporate
Bonds: A Reduced-Form Approach. London School of Economics
and Political Science, November
2005.
- How to Invest Optimally in Corporate
Bonds: A Reduced-Form Approach. International Conference
on Finance, Copenhagen, September 2005.
- On Life Insurance and Pension Insurance
Accounting and Solvency Standards. Nordea Investment
Management, Copenhagen, October 2004.
- Differential Systems in Life Insurance. 3rd
Conference in Actuarial Science and Finance on Samos, September 2004.
- Optimization in Life Insurance. 6th
World Congress of the Bernoulli Society for Mathematical Statistics and
Probability, Barcelona, July 2004.
- New Financial Products in Insurance. The 1st
Nordic summer school in insurance mathematics. Main lecturer (with T. Møller), Stockholm, September 2003.
- Optimization in Life Insurance. University
of Ulm, July 2003.
- Optimization in Life insurance. Technical
University Munich, July 2003.
- Quadratic Optimization of Life Insurance
Payment Streams. 7th International Congress on Insurance:
Mathematics and Economics, Lyon, June 2003.
- Optimization in Life Insurance. 2nd
Workshop on Dynamic Optimization Problems in Finance and Insurance,
Kaiserslautern, June 2003.
- On Merton's Problem for Life Insurers. Scientific
Conference on Insurance and Finance, Bonn, April 2003.
- Hvad laver de på
universitetet? - og hvad kan det bruges til? Den Danske Aktuarforening,
København, April 2003.
- Quadratic versus utility-based
optimization in life insurance. Workshop on stochastics
for risk, insurance and finance, London, December 2002.
- On Merton's problem for insurers. 6th International Congress on Insurance: Mathematics
and Economics, Lisbon, July 2002.
- On Merton's Problem for insurers.
Interplay between Mathematical Finance and Insurance, Århus,
June, 2002.
- Life insurance mathematics and
optimization. Fraunhofer ITWM, Kaiserslautern, June 2002.
- On jump-diffusion factor models with
intervention and Danish accounting practice. International
Symposium on Insurance and Finance,
Bergen, April
2002.
- Intervention options in life and pension
insurance. 12th AFIR Colloquium, Cancun, March 2002.
- Utility optimization of payment streams in
life and pension insurance. Workshop on stochastic control and its application
in insurance, Karlsruhe, December 2001.
- Aspekter af
værdifastsættelse i livs- og pensionsforsikring.
Nordea Markets, Copenhagen, October 2001.
- Intervention options in life and pension
insurance. 5th International Congress on Insurance: Mathematics
and Economics, PennState, Pennsylvania, July
2001.
- On valuation and control in life and
pension insurance. Ph.D. defense. Copenhagen, June 2001.
- Intervention options in life and pension
insurance. FML colloquium, Copenhagen, May 2001.
- Aspects of valuation in life insurance.
University of Southern Denmark, Odense, October 2000.
- Thiele's differential equation - still
going strong. The 1st T.N.Thiele
Symposium on Stochastic in Insurance and Finance, Copenhagen, August 2000.
- Contingent claims analysis in life and
pension insurance. 10th AFIR Colloquium, Tromsø,
June 2000.
- Contingent claims analysis in life and
pension insurance. University
of Oslo, January 2000.
- A financial approach to life and pension
insurance. ETH Zurich,
June 1999.
- A financial approach to life and pension
insurance. University
of Karlsruhe, July 1999.
Teaching
and supervision areas:
Life insurance mathematics and
- Life and Pension Insurance
- Personal Insurance
- Market Consistent
Valuation
- Pension Fund Management
- Mathematical
Finance
- Personal Finance
- Portfolio Optimization
- Credit Risk
Supervision (Ph.D.):
- Lars
Frederik Brandt Henriksen (in progress). (Supervised
jointly with Jesper Lund Pedersen)
- Kamille Sofie Tågholt (in progress). (Supervised
jointly with Jesper Lund Pedersen)
- Morten
Tolver Kronborg (in progress). (Supervised jointly with Søren Fiig Jarner and Michael Preisel,
ATP, industrial partner).
- Bruhn,
Kenneth (in progress). (Supervised
jointly with Per Klitgård and Per Linnemann) Subject: Insurance and Pension
Decision Making under Modern Notions of Preferences and Taxation
- Masotti, Esben Kryger (2010). Five Essays in Life Insurance
Mathematics. (Supervised
jointly with Søren Fiig
Jarner and Michael Preisel,
ATP, industrial partner).
- Nielsen, Peter Holm (2006). Financial Optimization Problems in Life
and Pension Insurance. (Supervised jointly with Hanspeter
Schmidli).
- Dahl, Mikkel (2005). On Mortality and
Investment Risk in Life Insurance. (Supervised jointly with Thomas Mikosch and Thomas Møller).
Supervision (Master/Cand.Act.):
- Eva Pedersen (in progress)
- Paul Membrere
(in progress)
- Cecilie Horn (in progress)
- Geske Kristensen (in progress)
- Nicholas Højer-Nielsen (March
26, 2012). Tarifering af Variable Annuiteter.
- Elisabeth Nærum
(December 19, 2011). Optimale investerings- og opsparingsstrategier med
endogen vanedannelse.
- Lukas Torp-Pedersen
(December 19, 2011). Endogeneous Habit
Formation.
- Sofie
Vester (December 13, 2011). (supervised
jointly with Mads Bryde
Andersen). Garantier i
pensionsaftaler.
- Catherine Louise Poulsen (October 10,
2011). (supervised jointly with Peter Holm
Nielsen). Kontributionsprincippet versus Gennemsnitsrenteprincippet.
- Søren
Skytte (October 3, 2011). Kontributionsprincippet.
- Kristian
Buchardt (September 19, 2011). (supervised jointly with Thomas Møller).
Affine Processes in Life Insurance Mathematics – With a View Towards Solvency II.
- Cathrine Renneberg (May 19, 2011). Værdifastsættelse af en
forsikringskontrakt med fokus på forsikringstagerens adfærd.
- Maj-Britt
Nordfang (March 22, 2011). Approximating optimal
investment strategies.
- Kamilla Petersen
(December 9, 2010). Inkonsistente porteføljeproblemer under kollektiv
potensnytte.
- Martine Stokholm
(September 27, 2010). Overskudsfordeling til homogene delbestande.
- Morten Tolver Kronborg
(September 23, 2010). Inkonsistente investerings- og forbrugsproblemer.
- Kirsten
Niels-Christiansen (September 23, 2010). Porteføljer og priser under middelværdi-varians
nytten med konstant og hyperbolsk risikoaversion.
- Christel Clausen
(September 23, 2010). Porteføljeproblemer med eksponentiel nytte of
kollektive objektfunktioner.
- Michael Hartvigsen Knudsen (September 7,
2010). Optimal Portfolios and utility indifference pricing under
mean-variance utility.
- Linda Maria Bodholdt (September 7, 2010). Optimeringsproblemer og
prisfastsættelse af ikke-hedgebare
forsikringskrav med mean-variance nytten.
- Agnieszka
Konicz (August 19, 2010). Performance
measurement of empirical and theoretical pension investment strategies.
- Iben
Jespersen (March 2, 2010). Optimal investment strategies for house owners.
- Thomas Styrk (2009). Time-homogeneous
optimal investment: Maximisation of expected utility of consumption and
minimisation of ruin probabilities.
- Michala
Holm Rode (2009). (supervised jointly with Peter Holm Nielsen and Thomas Møller). Nytteoptimering
med regime-skift, garantier og oplevelsesforsikring.
- Ieva
Masiulyte (2009). Dependent decrement theory in a
Markov chain framework.
- Kenneth Jensen (2009). Optimal Insurance and Consumption under
Changing Mortality.
- Diane Dross (2009). Portfolio Optimization under Market Crashes and
Liquidity Constraints.
- Kenneth Bruhn Kristiansen (2009). Optimal consumption, investment
and life annuity purchase under constraints for a single person and
multiple persons.
- Marie Refsgaard Sielemann (2009).
Porteføljeforsikringsstrategier på unit-link forsikringer.
- Hanne Kuckelhahn (2009). Quadratic
Hedging of Index Linked Life Insurance Contracts.
- Mads Hindkær Dahl
(2008). Optimal investering, forbrug og dødsfaldsydelse for husejere.
- Nichlas Abel Korsgaard (2008).
Risk and Cost Analysis of a Closed Life Insurance Portfolio.
- Peter Andersen (2008). Sammenligning af
strategier til afdækning af finansielle risici i et Black-Scholes
marked.
- Henrik Jespersen (2008). Bonusprognose.
- Morten Winther
(2008). (supervised jointly with Peter Fledelius). Risikomargen.
- Minna Ghasemi
(2008). (supervised jointly with Peter David
Melchior). VaR-based Valuation and Optimization.
- Lars Fogh Jensen (2008). Optimale
genforsikringsstrategier.
- Lise Jørgensen (2007). Optimale investeringsstrategier i
oplevelsesforsikringer.
- Rune Hove
Jacobsen (2007). Optimal Reinsurance of Life Insurance Risk in a Dynamic
Setting.
- Louise Kjellerup Eigtved
(2007). Betydningen af folkepension og beskatning i forbindelse med
beslutningsproblemer i livs- of
pensionsforsikring.
- Kristian
Smedemark Hasløv
(2007). (supervised jointly with Peter Holm
Nielsen). Porteføljeoptimering under stress.
- Katrine
Loug
(2006). Dynamisk versus statisk optimal investering.
- Julie Have (2005). Corporate Bond Prices in a Market with
Correlated Defaults.
- Lasse Jensen (2005).
Aktiv passiv modellering i forsikring.
- Helle
Simonsen (2005). Price Indexed Pension
Contracts.
- Anina
Grell (2005). Stopping Time Problems and
Stopping Games in Life Insurance.
- Jacob Bille (2005).
Værdifastsættelse i livsforsikring baseret på højere ordens momenter.
- Lars Keyper
Winkel (2005). (supervised
jointly with Jesper
Lund Pedersen), Prissætning af Unit-link forsikringer med særlige stiafhængige garantier.
- Jens Wissing
Jensen (2005). (supervised jointly
with Jesper Lund Pedersen), Unit-link produkter
baseret på ekstrema og fraktiler.
- Stine Breiner Andersen (2005). (supervised
jointly with Peter
Holm Nielsen), Optimale dækningsstrategier i livsforsikring.
- Rikke Schlüter Justesen
(2005). (supervised jointly
with Peter Holm Nielsen), Optimale
pensionsopsparingsstrategier.
- Jeanette Halle Larsen (2005). Fair fordeling af overskud i
livsforsikring.
- Stephan Waldstrøm (2004). Værdifastsættelse af en unit-link forsikring med en stiafhængig
garanti.
- Bitten Lind Nielsen
(2004). Stokastisk dødelighed for livrenter.
- Karen Skjøtt Christensen (2004). Asset Liability
Management - med fair parametre.
- David Melchior (2003).
Optimal allokering og udlodning af overskud i livsforsikring.
- Line Dahlbæk
Nielsen (2002). Analytiske resultater om genkøbs-
og fripoliceoptionen.
- Morten
Winther Hansen (2002). An Approximation Method
to Exercise and Surrender Options.
- Jeppe Ekstrøm (2001). Numerisk beregning af fair strategier
for investering og udbetaling af overskud.
Teaching (1997-2011):
- 10 courses on advanced life insurance
mathematics and mathematical finance (master courses)
- 10 courses on basic life insurance mathematics (3.
year bachelor courses)
- 5 courses on introductory insurance mathematics
(1. year bachelor courses)
- 7 optional courses on topics in finance and
life insurance (master courses)
(optimization
problems, optimal stopping, stochastic control, financial methods)