Related papers: Risk, utility and sensitivity to large losses

We study the properties of Expected Shortfall from the point of view of financial risk management. This measure --- which emerges as a natural remedy in some cases where Value at Risk (VaR) is not able to distinguish portfolios which bear…

Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff. Economic intuition suggests that…

A key issue in the estimation of energy hedges is the hedgers' attitude towards risk which is encapsulated in the form of the hedgers' utility function. However, the literature typically uses only one form of utility function such as the…

A Value-at-Risk based model is proposed to compute the adequate equity capital necessary to cover potential losses due to operational risks, such as human and system process failures, in banking organizations. Exploring the analogy to a…

We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to…

We derive a family of risk-sensitive reinforcement learning methods for agents, who face sequential decision-making tasks in uncertain environments. By applying a utility function to the temporal difference (TD) error, nonlinear…

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…

The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker's preferences. In order to obtain such utility values it is necessary to establish an analogy between…

Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function…

The utility-based shortfall risk (SR) measure introduced by Folmer and Schied [15] has been recently extended by Mao and Cai [29] to cumulative prospect theory (CPT) based SR in order to better capture a decision maker's utility/risk…

We study a general risk measure called the generalized shortfall risk measure, which was first introduced in Mao and Cai (2018). It is proposed under the rank-dependent expected utility framework, or equivalently induced from the cumulative…

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for…

We study submodularity for law-invariant functionals, with particular attention to convex risk measures. Expected losses are modular, and certainty equivalents are submodular exactly when the loss function is convex. Law-invariant coherent…

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak…

We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We…

We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose…

This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility…

We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto…

In economics, risk aversion is modeled via a concave Bernoulli utility within the expected-utility paradigm. We propose a simple test of expected utility and concavity. We find little support for either: only 30 percent of the choices are…

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call…