Related papers: A Stochastic Delay Model for Pricing Debt and Equi…
In this paper incomplete-information models are developed for the pricing of securities in a stochastic interest rate setting. In particular we consider credit-risky assets that may include random recovery upon default. The market…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a…
The standard formulation of Markov decision processes (MDPs) assumes that the agent's decisions are executed immediately. However, in numerous realistic applications such as robotics or healthcare, actions are performed with a delay whose…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
Parabolic partial differential equations (PDEs) are widely used in the mathematical modeling of natural phenomena and man made complex systems. In particular, parabolic PDEs are a fundamental tool to determine fair prices of financial…
This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional…
In software engineering, technical debt, signifying the compromise between short-term expediency and long-term maintainability, is being addressed by researchers through various machine learning approaches. This study seeks to provide a…
While defaults are rare events, losses can be substantial even for credit portfolios with a large number of contracts. Therefore, not only a good evaluation of the probability of default is crucial, but also the severity of losses needs to…
A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…
We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our…
In this paper we propose a new method of estimation for discrete choice demand models when individual level data are available. The method employs a two-step procedure. Step 1 predicts the choice probabilities as functions of the observed…
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…
A stochastic model with hidden discrete Markov processes is constructed to understand the behavior of debtors.
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…
We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem…
In this article we investigate the numerical solution of a scalar semilinear stochastic delay differential equation (SDDE) where the linear instantaneous feedback and nonlinear delayed feedback terms are perturbed by a pair of standard…