Related papers: Conditional Value-at-Risk Constraint and Loss Aver…
Having a perfect model to compute the optimal policy is often infeasible in reinforcement learning. It is important in high-stakes domains to quantify and manage risk induced by model uncertainties. Entropic risk measure is an exponential…
We apply the maximum entropy principle to economic systems in equilibrium and find the density function for the market's wealth. This is the same as price density which is used for insurance pricing. The risk aversion parameter of the agent…
Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…
To study the assumption that the utility maximization hypothesis implicitly adds to consumer theory, we consider a mathematical representation of pre-marginal revolution consumer theory based on subjective exchange ratios. We introduce two…
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 (1989), whereas the insurer is a (risk-averse or…
We consider a discrete-time version of the popular optimal dividend pay-out problem in risk theory. The novel aspect of our approach is that we allow for a risk averse insurer, i.e., instead of maximising the expected discounted dividends…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…
This paper introduces a rule for policy selection in the presence of estimation uncertainty, explicitly accounting for estimation risk. The rule belongs to the class of risk-aware rules on the efficient decision frontier, characterized as…
The extremum value theorem for function spaces plays the central role in optimal control. It is known that computation of optimal control actions and policies is often prone to numerical errors which may be related to computability issues.…
We present a new decision rule, \emph{maximin safety}, that seeks to maintain a large margin from the worst outcome, in much the same way minimax regret seeks to minimize distance from the best. We argue that maximin safety is valuable both…
This paper features expectiles in dynamic and stochastic optimization. Expectiles are a family of risk functionals characterized as minimizers of optimization problems. For this reason, they enjoy various unique stability properties, which…
This paper studies the behavior of a strategic aggregator offering regulation capacity on behalf of a group of distributed energy resources (DERs, e.g. plug-in electric vehicles) in a power market. Our objective is to maximize the…
Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an…
In this paper we extend the stability results of [4]}. Our utility maximization problem is defined as an essential supremum of conditional expectations of the terminal values of wealth processes, conditioned on the filtration at the…
We consider the worst-case expectation of a permutation invariant ambiguity set of discrete distributions as a proxy-cost for data-driven expected risk minimization. For this framework, we coin the term ordered risk minimization to…
Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex risk measures. Explicit solutions are found for…
In several applications such as clinical trials and financial portfolio optimization, the expected value (or the average reward) does not satisfactorily capture the merits of a drug or a portfolio. In such applications, risk plays a crucial…
Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes.…
Dynamic spectral risk measures define a claim's valuation bounds as supremum and infimum of expectations of the claim's payoff over a dominated set of measures. The measures at which such extrema are attained are called extreme measures. We…
People are often reluctant to sell a house, or shares of stock, below the price at which they originally bought it. While this is generally not consistent with rational utility maximization, it does reflect two strong empirical regularities…