Related papers: Large Portfolio Asymptotics for Loss From Default
We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model…
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…
We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal…
We discuss the parameter estimation of the probability of default (PD), the correlation between the obligors, and a phase transition. In our previous work, we studied the problem using the beta-binomial distribution. A non-equilibrium phase…
We propose two structural models for stochastic losses given default which allow to model the credit losses of a portfolio of defaultable financial instruments. The credit losses are integrated into a structural model of default events…
We consider a financial intermediary managing assets and liabilities exposed to several risk sources and seeking an optimal portfolio strategy to minimise the initial capital invested and the total risk associated with investment losses and…
We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error with respect to the small parameter defining the fast time…
We utilize the weak convergence method to establish the Freidlin--Wentzell large deviations principle (LDP) for stochastic delay differential equations (SDDEs) with super-linearly growing coefficients, which covers a large class of cases…
We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…
We analyze a class of nonlinear partial differential equations (PDEs) defined on $\mathbb{R}^d \times \mathcal{P}_2(\mathbb{R}^d),$ where $\mathcal{P}_2(\mathbb{R}^d)$ is the Wasserstein space of probability measures on $\mathbb{R}^d$ with…
We study a one-dimensional SDE that we obtain by performing a random time change of the backward Loewner dynamics in $\mathbb{H}$. The stationary measure for this SDE has a closed-form expression. We show the convergence towards its…
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…
We obtain the large deviation functional of a density profile for the asymmetric exclusion process of L sites with open boundary conditions when the asymmetry scales like 1/L. We recover as limiting cases the expressions derived recently…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…
The Law of Large Numbers tells us that as the sample size (N) is increased, the sample mean converges on the population mean, provided that the latter exists. In this paper, we investigate the opposite effect: keeping the sample size fixed…
The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and…
The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing…
Preferential attachment schemes, where the selection mechanism is linear and possibly time-dependent, are considered, and an infinite-dimensional large deviation principle for the sample path evolution of the empirical degree distribution…
This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward…