Related papers: Capital allocation for cash-subadditive risk measu…
In this paper, we study capital allocation for dynamic risk measures, with an axiomatic approach but also by exploiting the relation between risk measures and BSDEs. Although there is a wide literature on capital allocation rules in a…
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…
Risk measure is a fundamental concept in finance and in the insurance industry, it is used to adjust life insurance rates. In this current paper, we will study dynamic risk measures by means of backward stochastic Volterra integral…
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…
We discuss a general dynamic replication approach to counterparty credit risk modeling. This leads to a fundamental jump-process backward stochastic differential equation (BSDE) for the credit risk adjusted portfolio value. We then reduce…
A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub additive axiom to…
Capital allocation principles are used in various contexts in which a risk capital or a cost of an aggregate position has to be allocated among its constituent parts. We study capital allocation principles in a performance measurement…
We provide a new characterization of law-invariant backward stochastic differential equations (i.e. BSDEs) with quadratic growth. This answers the open question raised in Xu--Xu--Zhou (2022) on necessary conditions for law-invariance of…
Backward stochastic Volterra integral equations (BSVIEs in short) are studied. We introduce the notion of adapted symmetrical solutions (S-solutions in short), which are different from the M-solutions introduced by Yong [17]. We also give…
This paper is concerned with existence and uniqueness of M-solutions of backward stochastic Volterra integral equations (BSVIEs for short), which Lipschitz coefficients are allowed to be random, which generalize the results in [15]. Then a…
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…
Capital allocation is a procedure used to assess the risk contributions of individual risk components to the total risk of a portfolio. While the conditional tail expectation (CTE)-based capital allocation is arguably the most popular…
In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a…
This paper studies dynamic mean-variance (MV) asset allocation problems in general incomplete markets. Besides of the conventional MV objective on portfolio's terminal wealth, our framework can accommodate running MV objectives with general…
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…
Capital allocation is a procedure for quantifying the contribution of each source of risk to aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation under which the…
The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for…
We study two different contributions to the theory of (scalar) systemic risk measures. Namely the first aggregate or axiomatic approach and the first inject capital approach. For this purpose we establish a general framework, which is rich…
Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement for a large bank's trading book under the Basel 2.5 Accord…
In this paper, we establish existence, uniqueness, and regularity properties of the solutions to multi-dimensional backward stochastic Volterra integral equations (BSVIEs), whose (possibly random) generator reflects nonlinear dependence on…