Markov decision processes under model uncertainty

We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle, we obtain a local-to-global paradigm, namely solving a local, that is, a one time-step robust optimization problem leads to an optimizer of the global (i.e., infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the . We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.     

Optimal insurance under maxmin expected utility

We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the maxmin expected utility model of Gilboa and Schmeidler (J. Math. Econ. 18:141–153, 1989), whereas the insurer is a (risk-averse or risk-neutral) expected-utility maximiser. We characterise optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, of marginal utility of wealth, of belief heterogeneity, as well as of ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how a singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Rényi ambiguity set.