Kerem Ugurlu We study the utility maximization problem of a portfolio of one risky asset, a stock, and one riskless asset, a bond, under Knightian uncertainty on the drift term representing the long term growth rate of the risky asset. We further assume that the investor has a prior estimate about the drift term, so that we … Read more
We study Kusuoka representations of law invariant coherent risk measures on the space of bounded random variables. We refine this representation by giving that any law invariant coherent risk measure can be written as an integral of the Average Value-at-Risk measures on $[0,1]$, which gives a numerically constructive way to approximate any law invariant coherent … Read more
A new multivariate performance measure Average-Value-at-Risk, mAVaR αevaluating the sum of N risky assets composing the portfolio of an investor with respect to riskN-dimensional risk level vectorαis proposed. We show that the proposed operator satisfies the four axioms of a coherent risk measure, while reducing to the one variableAverage-Value-at-RiskAVaR, in caseN= 1. In that respect, … Read more
We study a robust optimal control of discrete time Markov chains with finite terminal T and bounded costs using probability distortion. The time inconsistency of these operators and hence its lack of dynamic programming are discussed. Due to that, dynamic versions of these operators are introduced and its availability for dynamic programming are demonstrated. Based … Read more
We give a finite state approximation scheme to countable state controlled robust/risk-averse Markov chains, where there is uncertainty in the transition probability. A convergence theorem along with the corresponding rate for this approximation is established. An approximation to the stationary optimal policy is also given. Our results show a fundamental difference between the finite state … Read more
We consider a continuous time Principal-Agent model on a finite time horizon, where we look for the existence of an optimal contract both parties agreed on. Contrary to the main stream, where the principal is modelled as risk-neutral, we assume that both the principal and the agent have exponential utility, and are risk averse with … Read more
We give explicit solutions for utility optimization problems in the presence of Knightian uncertainty in continuous time with nondominated priors and finite time horizon in a diffusion model. We assume that the uncertainty set is compact and time dependent on $[0,T]$. We solve the robust optimization problem explicitly both when the investor’s utility is of … Read more
We use Markov risk measures to formulate a risk averse version of a total cost problem on a controlled Markov process in infinite horizon. The one step costs are in $L^1$ but not necessarily bounded. We derive the conditions for the existence of the optimal strategies and present the robust dynamic programming equations. We illustrate … Read more
In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded L 1 -costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing a priori a global variable s heuristically, we show that there exist optimal policies for the infinite horizon … Read more
Two approaches to time consistency of risk averse multistage stochastic problems were dis- cussed in the recent literature. In one approach certain properties of the corresponding risk measure are postulated which imply its decomposability. The other approach deals directly with conditional optimality of solutions of the considered problem. The aim of this paper is to … Read more