For the solution Y of a multivariate random recurrence model Yn=AnYn-1+[zeta]n in we investigate the extremal behaviour of the process , , for with z*=1. This extends results for positive matrices An. Moreover, we obtain explicit representations of the compound Poisson limit of point processes...

This paper investigates the problem of hedging European call options using Leland's strategy in stochastic volatility markets with transaction costs. Introducing a new form for the enlarged volatility in Leland's algorithm, we establish a limit theorem and determine a convergence rate for the...

This paper investigates the problem of hedging European call options using Leland's strategy in stochastic volatility markets with transaction costs. Introducing a new form for the enlarged volatility in Leland's algorithm, we establish a limit theorem and determine a convergence rate for the...

We extend the resutls for the problem of option replication under proportional transaction costs in \cite{Nguyen} to more general frameworks where stochastic volatility and jumps are combined to capture market's important features. In particular, we study the hedging error due to discrete...

We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We compare the optimal solutions in form of optimal value,...

We investigate optimal consumption problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall for logarithmic utility functions. We find the solutions in terms of a dynamic strategy in explicit form, which can be compared and interpreted. This paper...

We consider the optimal investment problem for Black-Scholes type financial market with bounded VaR measure on the whole investment interval $[0,T]$. The explicit form for the optimal strategies is found.

We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads...

We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return $a$ and volatility $\sigma0$. If...