Related papers: Hedging under generalized good-deal bounds and mod…
In the paper we develop mathematical tools of quantile hedging in incomplete market. Those could be used for two significant applications: o calculating the \textbf{optimal capital requirement imposed by Solvency II} (Directive 2009/138/EC…
We consider a hidden-action principal-agent model, in which actions require different amounts of effort, and the agent privately knows his ability that determines his cost of effort. We show that linear contracts admit approximation…
We extend the study of [7, 18] to stochastic target problems with general market impacts. Namely, we consider a general abstract model which can be associated to a fully nonlinear parabolic equation. Unlike [7, 18], the equation is not…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
We study the pricing and the hedging of claim {\psi} which depends on the default times of two firms A and B. In fact, we assume that, in the market, we can not buy or sell any defaultable bond of the firm B but we can only trade…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
In many first-price auctions, bidders face considerable strategic uncertainty: They cannot perfectly anticipate the other bidders' bidding behavior. We propose a model in which bidders do not know the entire distribution of opponent bids…
We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived…
In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables…
Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multi-period settings. Current approaches model uncertainty either…
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the…
Risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as, more or less consciously, in our everyday life. We present a discussion of the characterization of risks and of the…
Building on the work of Schweizer (1995) and Cern and Kallseny (2007), we present discrete time formulas minimizing the mean square hedging error for multidimensional assets. In particular, we give explicit formulas when a regime-switching…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment…
We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and…
We introduce a general decision tree framework to value an option to invest/divest in a project, focusing on the model risk inherent in the assumptions made by standard real option valuation methods. We examine how real option values depend…
We consider hedging of a contingent claim by a 'semi-static' strategy composed of a dynamic position in one asset and static (buy-and-hold) positions in other assets. We give general representations of the optimal strategy and the hedging…
We consider the mean-variance hedging problem under partial Information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is…