The paper is devoted to modeling optimal exercise strategies of the behavior of investors and issuers working with convertible bonds. This implies solution of the problems of stock price modeling, payoff computation and ...

An exponential estimate of ruin probability for an insurance company which invests all its capital in risk assets is found. The process which describes the risky assets is assumed to follow a geometrical Brownian motion. ...

Asymptotic expansions for the distribution of the surplus prior to and at the time of a ruin are given for nonlinearly perturbed risk processes.

We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector θ to be estimated that also appears in the distribution of the regressor variable x. The estimation of θ is based ...

The asymptotic behavior of the general type third order autonomous oscillating system under the action of small non-linear random perturbations of ”white” and ”Poisson” types is investigated.

The problem considered is the problem of optimal linear estimation of the functional Aξ = ∑↑∞↓j=0 ∫↓G a(g, j)ξ(g, j)dg which depends on the unknown values of a homogeneous random field ξ(g, j) on the group G × Z from ...

A theorem is proved that allows to use approximations for construction of the Karhunen-Loeve model of stochastic process with known correlation function.

The paper is devoted to the problem of establishing the conditions on the stochastic process to belong it to the functional space Lq(R) with probability one. The corresponding results were obtained for the strictly Orlicz, ...

American options give us the possibility to exercise them at any moment of time up to maturity. An optimal stopping domain for American type options is a domain that, if the underlying price process enters we should exercise ...

Necessary and sufficient conditions for weak convergence of first-rareevent times for semi-Markov processes with finite set of states in series of schemes are obtained.