相关论文: Managing counterparty credit risk via BSDEs

In this paper, we consider dynamic risk measures induced by backward stochastic differential equations (BSDEs). We discuss different examples that come up in the literature, including the entropic risk measure and the risk measure arising…

This paper is devoted to proposing a new asymmetric risk-sensitive criterion involving different risk attitudes toward varying risk sources. The criterion can only be defined through the initial value of the minimal solutions of quadratic…

We study dynamic hedging of counterparty risk for a portfolio of credit derivatives. Our empirically driven credit model consists of interacting default intensities which ramp up and then decay after the occurrence of credit events. Using…

In this paper, we provide a representation theorem for dynamic capital allocation under It{\^o}-L{\'e}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with…

We introduce the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk measure recovers, i.e., bounces back, when the risk-acceptance set is breached. We develop the corresponding…

This work deals with backward stochastic differential equation (BSDE) with random marked jumps, and their applications to default risk. We show that these BSDEs are linked with Brownian BSDEs through the decomposition of processes with…

We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems…

We study an optimal investment problem under contagion risk in a financial model subject to multiple jumps and defaults. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the…

The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of…

We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows…

The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [Han, Jentzen and E, PNAS, 115(34):8505-8510, 2018] has shown great…

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…

In this paper, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method…

Backward Stochastic Differential Equations (BSDEs) have been widely employed in various areas of social and natural sciences, such as the pricing and hedging of financial derivatives, stochastic optimal control problems, optimal stopping…

For an $\cF_T$-measurable payoff of a European type contingent claim, the recursive utility process/dynamic risk measure can be described by the adapted solution to a backward stochastic differential equation (BSDE). However, for an…

This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia…

This paper establishes characterization results for dynamic return and star-shaped risk measures induced via backward stochastic differential equations (BSDEs). We first characterize a general family of static star-shaped functionals in a…

The aim of this paper is to study an optimal stopping problem for dynamic risk measures induced by backward stochastic differential equations with jumps and delayed generator. Firstly, we connect the value function of this problem to…

In the context of risk measures, the capital allocation problem is widely studied in the literature where different approaches have been developed, also in connection with cooperative game theory and systemic risk. Although static capital…

In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic…