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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Weak solutions of stochastic differential inclusions and their compactness

100%
Michta M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2009
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tom 29
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nr 1
91-106
EN
In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.
2
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On risk reserve under distribution constraints

100%
Michta M.
Discussiones Mathematicae Probability and Statistics
|
2000
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tom 20
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nr 2
249-260
EN
The purpose of this work is a study of the following insurance reserve model: $R(t) = η + ∫_{0}^{t} p(s,R(s))ds + ∫_{0}^{t} σ(s,R(s))dW_{s} - Z(t)$, t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: $inf_{0≤t≤T} P{R(t) ≥ c} ≥ γ$ is considered.
3

Set-valued random differential equations in Banach space

100%
Michta M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
|
tom 15
|
nr 2
191-200
EN
We consider the problem of the existence of solutions of the random set-valued equation: (I) $D_HX_t = F(t,X_t)P.1$, t ∈ [0,T] -a.e.; X₀ = U p.1 where F and U are given random set-valued mappings with values in the space $K_c(E)$, of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.
4

Note on the selection properties of set-valued semimartingales

100%
Michta M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1996
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tom 16
|
nr 2
161-169
EN
Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.
5
Content available remote

Optimal solutions to stochastic differential inclusions

100%
Michta M.
Applicationes Mathematicae
|
2002
|
tom 29
|
nr 4
387-398
EN
A martingale problem approach is used first to analyze compactness and continuous dependence of the solution set to stochastic differential inclusions of Ito type with convex integrands on the initial distributions. Next the problem of existence of optimal weak solutions to such inclusions and their dependence on the initial distributions is investigated.
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