Serguei Pergamenshchikov

In the insurance business risky investments are dangerous

Abstract. We find an exact asymptotics of the ruin probability

In the insurance business risky investments are dangerous: the case of negative risk sums

\Psi (u)

Optimal consumption and investment for markets with random coefficients

when the capital of insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a and volatility

Robust adaptive efficient estimation for semi-Markov nonparametric regression models

\sigma>0

Approximate hedging problem with transaction costs in stochastic volatility markets

. In contrast to the classical case of non-risky investments where the ruin probability decays exponentially as the initial endowment u tends to infinity, in this model we have, if

Oracle inequalities for the stochastic differential equations

\rho:=2a/\sigma^2>1

The Optimal Investment and Consumption for Financial Markets Generated by the Spread of Risky Assets for the Power Utility

, that

Sequential

\Psi(u)\sim Ku^{1-\rho}

\delta

for some

-Optimal Consumption and Investment for Stochastic Volatility Markets with Unknown Parameters

K>0