This article contains datasets related to the research article titled a novel jump diffusion model based on SGT distribution and its applications ("A novel jump diffusion model based on SGT distribution and its applications" (W.J. Xu, G.F. Liu, H.Y. Li, 2016) [1]). The datasets contain continuous composite daily percentage return values which are computed from the daily closing prices. Firstly,...

Recent development in ruin theory has seen growing popularity of jump diffusion processes in modeling an insurer’s assets and liabilities. Despite the variations of technique, the analysis of ruin-related quantities mostly relies on solutions to certain differential equations. In this paper, we propose in the context of Lévy-type jump diffusion risk models a solution method to a general class o...

In this paper we demonstrate the efficacy of a stochastic modelling approach involving both diffusion and a jump processes to describe the evolution of spot electricity prices in New South Wales. The model allows a deterministic time trend component and an unobserved process driven by both time varying volatility and occasional jumps. The structure allows us to cast the problem in a state space...

This paper considers an ?-robust optimal investment problem for a defined contribution (DC) pension plan with uncertainty about jump and diffusion risks in mean-variance framework. Our model allows the manager to have different levels of ambiguity aversion, rather than only consider extremely ambiguity-averse attitude. Moreover, DC plan, contributions are supposed be predetermined amount money ...

This thesis is a study of approximation and calibration of stochastic processes with applications in finance. It consists of an introduction and four research papers. The introduction is as an overview of the role of mathematics in certain areas of finance. It contains a brief introduction to the mathematical theory of option pricing, as well as a description of a mathematical model of a financ...

We formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model’s parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on t...

Let Z t,z be a R -valued jump diffusion controlled by ν with initial condition Z t,z(t) = z. The aim of this paper is to characterize the set V (t) of initial conditions z such that Z t,z can be driven into a given target at a given time by proving that the function u(, z) = 1 − 1V (t) satisfies, in the viscosity sense, the equation (2) below. As an application, we study the problem of hedging ...

We present a multi-dimensional jump-diffusion version of a structural default model and show how to use it in order to value the credit value adjustment for a credit default swap. We develop novel analytical and numerical methods for solving the corresponding boundary value problem with a special emphasis on the role of negative asset value jumps. Using recent market data, we show that under re...

The basic contracts traded on energy exchanges are swaps involving the delivery of electricity for fixed-rate payments over a certain period of time. The main objective of this article is to solve the quadratic hedging problem for European options on these swaps, known as electricity swaptions. We consider a general class of Hilbert space valued exponential jump-diffusion models. Since the forw...

This study investigates the optimal switching boundary to a renewable fuel when oil prices exhibit continuous random fluctuations along with occasional discontinuous jumps. In this paper, oil prices are modeled to follow jump diffusion processes. A completeness result is derived. Given that the market is complete the value of a contingent claim is risk neutral expectation of the discounted pay ...