Related papers: Integrals of Higher Binary Options and Defaultable…
The prediction of a binary sequence is a classic example of online machine learning. We like to call it the 'stock prediction problem,' viewing the sequence as the price history of a stock that goes up or down one unit at each time step. In…
In this paper, an integral equation representation for the early exercise boundary of an American option contract is considered. Thus far, a number of different techniques have been proposed in the literature to obtain a variety of integral…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
We study non-linear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and p default martingales. The driver of the BSDE with multiple default jumps can take a generalized form involving an optional finite…
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of…
In this work, a pricing model for a defaultable corporate bond with credit rating migration risk is established. The model turns out to be a free boundary problem with two free boundaries. The latter are the level sets of the solution but…
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential L\'evy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent L\'evy measure.…
We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReLU architectures capable of efficiently approximating tensor…
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation)…
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time…
No--arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist among different markets in various fields, even for a very short time. By knowing that an arbitrage property exists,…
We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black-Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an…
We propose a numerical procedure for computing the prices of European options, in which the underlying asset price is a Markovian strict local martingale. If the underlying process is a strict local martingale and the payoff is of linear…
In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in…
This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…
The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general c{\`a}dl{\`a}g martingales. When the martingale is a standard Brownian motion,…
This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative…
We study the optimal bailout dividend problem with transaction costs for an insurance company, where shareholder payouts align with the arrival times of an independent Poisson process. In this scenario, the underlying risk model follows a…