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Dual risk models are popular for modeling a venture capital or high tech company, for which the running cost is deterministic and the profits arrive stochastically over time. Most of the existing literature on dual risk models concentrated…
In this paper monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity…
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach…
We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these…
The aim of these lectures at MITACS-PIMS-UBC Summer School in Risk Man- agement and Risk Sharing is to discuss risk controlled approaches for the pricing and hedging of financial risks. We will start with the classical dual approach for…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic…
Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable…
This paper characterizes the equilibrium in a continuous time financial market populated by heterogeneous agents who differ in their rate of relative risk aversion and face convex portfolio constraints. The model is studied in an…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex…
We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good…
The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…
We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…
A fundamental problem in risk management is the robust aggregation of different sources of risk in a situation where little or no data are available to infer information about their dependencies. A popular approach to solving this problem…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these…
This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in 1976. We derive an explicit dual problem in terms of two dual variables, one of which is the…
This paper presents a novel two-stage optimization framework designed to model integrated quantile functions, which leads to the formulation of a bilinear optimization problem (P). A specific instance of this framework offers a new approach…
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…