Constrained portfolios in incomplete markets: a dynamic programming approach to Heston’s model
Seminar in Insurance and Economics
SPEAKER: Yevhen Havrylenko (TUM).
TITLE: Constrained portfolios in incomplete markets: a dynamic programming approach to Heston’s model.
ABSTRACT: This talk is centered on the dynamic portfolio optimization with terminal-wealth constraints. We start with an overview of the seminal paper Kraft & Steffensen (2013), where the authors generalize the dynamic programming approach to optimal-investment problems with terminal-wealth constraints in a complete Black-Scholes market. Building on that, we extend the dynamic programming approach to constrained problems in incomplete markets due to stochastic volatility. We demonstrate that the value function in the constrained problem can be represented as an expected modified utility of a vega-neutral financial derivative on the optimal unconstrained wealth. The optimal wealth and the optimal investment strategy in the constrained problem follow similarly. We show the details using the example of a power-utility maximizing investor with a Value-at-Risk constraint. At the end of the talk, we briefly discuss the results of the corresponding numerical studies where we substantiate the impact of risk aversion levels, and investment horizons on the optimal investment strategy. The talk in based on the working paper Escobar-Anel, Havrylenko, Zagst (2022).
Kraft, H., & Steffensen, M. (2013). A dynamic programming approach to constrained portfolios. European Journal of Operational Research, 453–461. https://doi.org/10.1016/j.ejor.2013.02.039.
Escobar-Anel, M., Havrylenko, Y., and R. Zagst (2022). “Constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model”. Working paper. https://doi.org/10.48550/arXiv.2208.14152.