Computational Finance
Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the…
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance…
We study two classes of over-the-counter markets specified by systems of ODE's, in the spirit of Duffie-Garleanu-Pedersen, Econometrica, 2005. We first compute the steady states for many of these ODE's. Then we obtain the prices at which…
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the…
In this paper we explore an identity in distribution of hitting times of a finite variation process (Yor's process) and a diffusion process (geometric Brownian motion with affine drift), which arise from various applications in financial…
A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely applied investment strategy in the financial industry. Recently, Ekstr\"om, Lindberg and Tysk studied the problem of…
This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence,…
In the aftermath of the global financial crisis, much attention has been paid to investigating the appropriateness of the current practice of default risk modeling in banking, finance and insurance industries. A recent empirical study by…
This appendix proves CORN's universal consistency. One of Bin's PhD thesis examiner (Special thanks to Vladimir Vovk from Royal Holloway, University of London) suggested that CORN is universal and provided sketch proof of Lemma 1.6, which…
Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a…
Online portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning, and data mining,…
This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for…
This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where…
We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry…
The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making…
We propose a new Quantization algorithm for the approximation of inhomogeneous random walks, which are the key terms for the valuation of CDO-tranches in latent factor models. This approach is based on a dual quantization operator which…
This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive…
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model…
Motivated by applications to bond markets, we propose a multivariate framework for discrete time financial markets with proportional transaction costs and a countable infinite number of tradable assets. We show that the no-arbitrage of…