Consider a non-symetric generalized diffusion X(·) in R d determined by the differential operator A(x) = − ij ∂iaij (x)∂j + i bi(x)∂i. In this paper the diffusion process is approximated by Markov jump processes Xn(·) in homogeneous and isotropic grids Gn ⊂ R d which converge in distribution to diffusion. The generators of Xn(·) are constructed explicitly. Due to the homogeneity and isotropy of...

We have derived reaction-dispersal-aggregation equations from Markovian reaction-random walks with density-dependent jump rate or density-dependent dispersal kernels. From the corresponding diffusion limit we recover well-known reaction-diffusion-aggregation and reaction-diffusion-advection-aggregation equations. It is found that the ratio between the reaction and jump rates controls the onset ...

For a certain scalar linear jump-diffusion stochastic differential equation (jump SDE) the asymptotic stability (i.e. convergence to zero as time t → ∞) is considered. Using the jump SDE as a test equation, two types of ‘balanced’ numerical methods are evaluated with respect to computational stability. For both methods it is shown by an analysis that for sufficiently small time steps the numeri...

In this paper we give the closed form solution of some optimal stopping problems for processes derived from a diffusion with jumps. Within the possible applications, the results can be interpreted as pricing perpetual American Options under diffusion-jump information.

In the inference for jump-diffusion processes, we often need to get the information of the jump part and of the continuous part separately from the data. Although some asymptotic theories have been studied on this issue, a practical interest is the inference from finitely many discrete samples. In this paper we propose a numerical procedure to construct a filter to judge whether or not a jump o...

Abstract In this paper, we consider the classical problem of utility maximization in a financial market allowing jumps. Assuming that the constraint set is a compact set, rather than a convex one, we use a dynamic method from which we derive a specific BSDE. This being done, we aim at showing existence and uniqueness results for the introduced BSDE. This allows us finally to give an “explicit” ...

In this paper, we study the optimal investment strategy for a defined contribution pension plan under jump diffusion model and S-shaped utility. We assume that members can invest their fund in financial market consisting of risk-free asset risk whose price process follows process. The goal managers is to maximize expected utility real terminal wealth apply Lagrange dual method, concavification ...

Derivatives are alternative financial instruments which extend traders opportunities to achieve some financial goals. They are risk management instruments that are related to a data in the future, and also they react to uncertain prices. Study on pricing futures can provide useful tools to understand the stochastic behavior of prices to manage the risk of price volatility. Thus, this study eval...

Using 5-minute high frequency data from the Chinese stock market, we employ a non-parametric method to estimate Fama-French portfolio realized jumps and investigate whether the estimated positive, negative and sign realized jumps could forecast or explain the cross-sectional stock returns. The Fama-MacBeth regression results show that not only have the realized jump components and the continuou...

The Federal Reserve adjusts the federal funds target rate discretely, causing discontinuity in short-term interest rates. Unlike Poisson jumps, these adjustments are well anticipated by the market. We propose a term structure model that incorporates an anticipated jump component with known arrival times but random jump size. We find that doing so improves the model performance in capturing the ...