6 papers
Boundary Approximation for Sticky Jump-Reflected Processes on the Half-Line
Andrey Pilipenko, Andrey Sarantsev
The Skorokhod reflection was used in 1961 to create a reflected diffusion on the half-line. Later, it was used for processes with jumps such as reflected Lévy processes. Like a Bro…
IID Time Series Testing
Andrey Sarantsev
Traditional white noise testing, for example the Ljung-Box test, studies only the autocorrelation function (ACF). Time series can be heteroscedastic and therefore not i.i.d. but st…
Optimal Portfolio with Power Utility of Absolute and Relative Wealth
Andrey Sarantsev
Portfolio managers often evaluate performance relative to benchmark, usually taken to be the Standard & Poor 500 stock index fund. This relative portfolio wealth is defined as the…
A Note on Subexponential Rate of Convergence to Equilibrium for Processes on the Half-Line
Andrey Sarantsev
A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions…
Exponential convergence rate of ruin probabilities for level-dependent Lévy-driven risk processes
Pierre-Olivier Goffard, Andrey Sarantsev
We explicitly find the rate of exponential long-term convergence for the ruin probability in a level-dependent Lévy-driven risk model, as time goes to infinity. Siegmund duality al…
Explicit Rates of Exponential Convergence for Reflected Jump-Diffusions on the Half-Line
Andrey Sarantsev
Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the ra…