Related papers: A Stochastic Delay Model for Pricing Debt and Equi…
This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…
Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…
We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages:…
We model the stock price dynamics through a semi-Markov process obtained using a Poisson random measure. We establish the existence and uniqueness of the classical solution of a non-homogeneous terminal value problem and we show that the…
The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap between these fields. In this paper, we develop a continuous…
In this work, I generalize Merton's approach of pricing risky debt to the case where the interest rate risk is modeled by the CIR term structure. Closed form result for pricing the debt is given for the case where the firm value has…
The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\'evy LIBOR model of Eberlein and \"Ozkan (2005). Standard methods can be applied to solve the stochastic…
In this letter, I consider the issue of pricing risky debt by following Merton's approach. I generalize Merton's results to the case where the interest rate is modeled by the CIR term structure. Exact closed forms are provided for the risky…
We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by…
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…
We introduce and compare two domain decomposition based numerical methods, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation methods (DNWR and NNWR respectively), tailored for solving partial differential equations (PDEs)…
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
The objective is to develop a general stochastic approach to delays on financial markets. We suggest such a concept in the context of large platonic markets, which allow infinitely many assets and incorporate a restricted information…
This article proposes a method for measuring the latent risks involved in the recovery process of non performing loans in financial institutions and business firms that deal with collection and recovery processes. To that end, we apply the…
This paper presents a discrete--time equity derivatives pricing model with default risk in a no--arbitrage framework. Using the equity--credit reduced form approach where default intensity mainly depends on the firm's equity value, we…
In this paper, we introduce a model that adds a non-linearity to discounting: the discounting factor may depend on the notional (i.e., discounted values are no longer linear in the notional). In the first part of the paper, we provide a…
Several real-world scenarios, such as remote control and sensing, are comprised of action and observation delays. The presence of delays degrades the performance of reinforcement learning (RL) algorithms, often to such an extent that…
Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized…
In this study, we introduce new estimation methods for the required rate of return of the stochastic dividend discount model (DDM) and the private company valuation model, which will appear below. To estimate the required rate of return, we…