In-Suk Wee

Asymptotic Behavior of Loss Probability in GI/M/1/K Queue as K Tends to Infinity

We obtain an asymptotic behavior of the loss probability for the GI/M/1/K queue as K→∞ for cases of ρ<1, ρ>1 and ρ=1.

Stability for multidimensional jump-diffusion processes

The aim of this work is to obtain sufficient conditions for stability of multidimensional jump-diffusion processes in the sense of stability in distribution and stability at the equilibrium solution. The technique employed is to construct appropriate Lyapunov functions.

Lower functions for processes with stationary independent increments

SummaryLet {Xt} be aR1-valued process with stationary independent increments and

The law of the iterated logarithm for local time of a Lévy process

A_t = \mathop {\sup }\limits_{s \leqq t} |X_s |

Lower functions for asymmetric Lévy processes

. In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing functionh(t) such that lim infAt/h(t)=C a.s. ast→0 andt→∞, for some positive finite constantC whenh(t) takes a particular form. Also two analytic conditions are considered as application.

Asymptotic analysis of loss probability in a finite queue where one packet occupies as many places as its length

We consider a jump-diffusion model for asset price which is described as a solution of a linear stochastic differential equation driven by a Lévy process. Such a market is incomplete and there are many equivalent martingale measures. We price a contingent claim with respect to the minimal martingale measure and construct a hedging strategy for the contingent claim in the locally risk-minimizing sense. We study the problem of convergence of option prices jointly with the costs from the locally risk-minimizing strategies when the jump-diffusion models converge to the Black–Scholes model.

Upper functions for lévy processes having only negative jumps

SummaryLet {Xt} be a one-dimensional Lévy process with local timeL(t, x) andL*(t)=sup{L(t, x): x ∈ ℝ}. Under an assumption which is more general than being a symmetric stable process with index α>1, we obtain a LIL forL*(t). Also with an additional condition of symmetry, a LIL for range is proved.

ERROR ESTIMATES FOR OPTION PRICES IN JUMP-DIFFUSION MODELS

The purpose of this work is to obtain sufficient conditions for transience and recurrence of multidimensional jump–diffusion processes, which are driven by Brownian motion and Poisson random measure. The approach adopted here is to construct appropriate Lyapounov functions