TD-05: Optimal Control and Optimization in Economics, Finance and Management I
Stream: Optimal Control and Optimization in Economics, Finance and Management
Room: Pontryagin
Chair(s): Ioannis Baltas

Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market
Gerhard-Wilhelm Weber, Emel Savku
We apply dynamic programming principle to discuss two optimal investment problems by using zero-sum and nonzero-sum stochastic game approaches in a continuous-time Markov regime-switching environment. The first application is a zero-sum game between an investor and the market, and the second one formulates a nonzero-sum stochastic differential portfolio game as the sensitivity of two investors’ terminal gains. We derive regime-switching Hamilton-Jacobi-Bellman-Isaacs equations and obtain explicit optimal portfolio strategies with Feynman-Kac representations of value functions.

Random oligopolistic market optimal equilibrium control problem
Annamaria Barbagallo
The aim of the talk is to analyze the policymaker’s point of view of the random oligopolistic market equilibrium problem and present a stochastic optimal control equilibrium problem. More precisely, we study a model in which control policies may be imposed to regulate the amounts of exportation in random way. Control policies are implemented by imposing higher taxes or subsidies in order to restrict or encourage the exportation. We prove that the system that controls the commodity exportations in random way is expressed by a stochastic inverse variational inequality.

Optimal management of Defined Contribution pension funds during the distribution phase under the effect of inflation, mortality and uncertainty
Ioannis Baltas, Athanasios Yannacopoulos, Gerhard-Wilhelm Weber
We study the problem of optimal management of defined contribution (DC) pension funds, during the distribution phase, within a model uncertainty framework by taking into account the effect of (i) inflation and (ii) mortality. By employing robust control and dynamic programming techniques, we provide closed form solutions for the case of the exponential utility function. Moreover, we provide a detailed study of the limiting behavior of the associated stochastic differential game. Finally, we present a novel numerical approach that elucidates the effect of robustness and inflation.