PhD Defense Julie Bjørner Søe
Title: Benefit and pension planning based on the (inhomogeneous) preferences of the policyholder
Abstract:
This thesis consists of independent investigations related to benefit and pension planning based on policyholders’ inhomogeneous preferences. The first four chapters are centered around the assumption of time-additive preferences, and the last three chapters include the concept of time inconsistency in optimization problems. The chapters are linked by the shared objective of understanding policyholders’ decisions and preferences to better design, manage, and advise on life insurance and savings products.
Chapter 1 provides the reader with background while easing into the general topic of the thesis and provides the main contributions for Chapters 2, 3, and 4.
In Chapter 2, containing the manuscript Optimal consumption, investment, and insurance under state-dependent risk aversion, we formalize and solve the problem of optimal consumption, investment, and life insurance decisions with state-dependent risk aversion, where the states can represent the biometric states of a policyholder.
Using a multi-state Markov chain model to describe the states, we construct the value function by aggregating value functions of underlying sub-problems, where each sub-problem represents a state. We illustrate numerically the optimal decisions in a three-state disability model of a single policyholder, demonstrating the effect on optimal controls by changes in preferences.
Chapter 3, investigates the possibility of handling state-dependent utility, where the state is the underlying state of the market, by adjusting for risk we measure at time zero the utility of a financial value of a payment at a future time t. Consequently, we acknowledge that the preferences of policyholders may evolve in response to changes in the underlying market conditions. We introduce a deflator that accounts for both financial and actuarial risks. We solve the problem of optimal consumption, investment, and life insurance in this deflated setting by using dynamic programming
and providing explicit solutions for CRRA utility functions.
In Chapter 4, we establish a link to the practical usage of optimal controls in the industry by evaluating policyholders’ perceptions of their life insurance coverages. In Implicit Prioritization of Life Insurance Coverage: A Study of Customer Preferences in PFA Pension we compare the choices and preferences for an entire portfolio with data supplied by PFA Pension.
In the last three chapters, we study two seemingly different utility optimization problems, both in the context of time inconsistency issues handled using equilibrium theory. Chapter 5 introduces and eases the reader into the context of time-inconsistent preferences and provides the main contributions from Chapters 6 and 7. In Chapter 6, we examine the value of the annuity market in the decumulation phase of a pension plan for an investor who either experiences time-additive preferences or separates the preferences of risk aversion and elasticity of inter-temporal substitution. What is the value of the annuity market? characterizes the relative loss of wealth by losing access to annuities, and numerical examples illustrate the results.
In the last chapter, Optimal Equilibrium Investment and Insurance with State Dependent Risk Aversion, we investigate the optimal equilibrium investment and insurance strategies, with state-dependent risk aversion as in Chapter 2, but incorporating uncertainty and randomness in the preferences and evaluating certainty equivalents resulting in a time-inconsistent optimization problem. We handle this by applying the equilibrium approach, presenting a verification solutions for different utility functions.
Supervisor: Professor Mogens Steffensen, University of Copenhagen
Assessment committee:
Professor Jostein Paulsen (chairperson), University of Copenhagen
Associate Professor Sascha Desmettre, University of Linz
Associate Professor Anne G. Balter, Tilburg University