31 citations · 137 across the 73 of their papers we have counts for
18 papers · 1 filter
On stochastic integrals with controlled growth of their containing range
Nikolai Dokuchaev
This short note suggests special examples of stochastic Ito integrals with controlled growth of their containing range. The integrands for this integrals are presented explicitly.…
On recovering solutions for SPDEs from their averages
Nikolai Dokuchaev
We study linear stochastic partial differential equations of parabolic type. We consider a new boundary value problem where a Cauchy condition is replaced by a prescribed average o…
A smooth component of the fractional Brownian motion and optimal portfolio selection
Nikolai Dokuchaev
We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two in…
On the fractional stochastic integration for random non-smooth integrands
Nikolai Dokuchaev
The paper suggests a way of stochastic integration of random integrands with respect to fractional Brownian motion with the Hurst parameter H> 1/2. The integral is defined initiall…
A pathwise inference method for the parameters of diffusion terms
Nikolai Dokuchaev
We consider inference of the parameters of the diffusion term for Cox-Ingersoll-Ross and similar processes with a power type dependence of the diffusion coefficient from the underl…
On forward and backward SPDEs with non-local boundary conditions
Nikolai Dokuchaev
We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the termin…
Degenerate backward SPDEs in domains: non-local boundary conditions and applications to finance
Nikolai Dokuchaev
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the…
Backward SPDEs with non-local in time and space boundary conditions
Nikolai Dokuchaev
We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a function…
Boundary value problems for functionals of Ito processes
Nikolai Dokuchaev
Backward stochastic partial differential equations in bounded and unbounded domains are studied. Existence and regularity results are obtained. Duality relationship with forward SP…
On almost surely periodic and almost periodic solutions of backward SPDEs
Nikolai Dokuchaev
We study linear backward stochastic partial differential equations of parabolic type with special boundary conditions in time. The standard Cauchy condition at the terminal time is…
Duality and semi-group property for backward parabolic Ito equations
Nikolai Dokuchaev
We study existence, uniqueness, semi-group property, and a priori estimates for solutions for backward parabolic Ito equations in domains with boundary. We study also duality betwe…
Representation of functionals of Ito processes and their first exit times
Nikolai Dokuchaev
The representation theorem is obtained for functionals of non-Markov processes and their first exit times from bounded domains. These functionals are represented via solutions of b…
On -distance between first exit times from two regions
Nikolai Dokuchaev
First exit times from regions and their dependence on variations of boundaries are discussed for diffusion processes. The paper presents an estimate of -distance between exit…
Optimal portfolio selection and compression in an incomplete market
Nikolai Dokuchaev, Ulrich Haussmann
We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the m…
Maximin setting for investment problems and fixed income management with observable but non-predictable parameters
Nikolai Dokuchaev
We study optimal investment problem for a diffusion market consisting of a finite number of risky assets (for example, bonds, stocks and options). Risky assets evolution is describ…
Pricing rule based on non-arbitrage arguments for random volatility and volatility smile
Nikolai Dokuchaev
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices.…
A paradox of diffusion market model related with existence of winning combinations of options
Nikolai Dokuchaev
We consider strategies of investments into options and diffusion market model. It is shown that there exists a correct proportion between "put" and "call" in the portfolio such tha…
A new property of absorbed diffusions
Nikolai Dokuchaev
We consider stochastic diffusion processes absorbed at the boundary of a domain. It is shown that there exist initial distributions which ensure a given decreasing of density of th…