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Optimization of the flow of dividends. (English. Russian original) Zbl 0878.90014
Russ. Math. Surv. 50, No. 2, 257-277 (1995); translation from Usp. Mat. Nauk 50, No. 2, 25-46 (1995).
The authors consider the Radner-Shepp model, $$dX_t=\mu dt+ \sigma dW_t-dZ_t$$ assuming that $$(\mu,\sigma)$$ are the values in an a priori admissible set $$A$$, where $$A$$ is an element, $$A=\{(\mu,\sigma)\}$$; $$\mu>0$$; $$\sigma>0$$, and the processes $$Z=(Z_t)_{t\geq 0}$$ are such that:
(A) $$dZ_t= u(X_t)dt$$, where $$=u=u(x)$$, $$Z_0=Z_0(x)$$ are arbitrary measurable functions $$0\leq u(x)\leq K<\infty$$, $$0\leq Z_0(x)\leq x$$.
(B) $$Z_t= \sum_{i\geq 0}e^{-\lambda T_i}z_iI$$ $$(T\leq t)$$, where $$0=T_0< T_1< T_2<\dots$$ are random moments of payments of dividends and $$\{z_i\}$$ are non-negative amounts of dividends paid.
(C) The process, $$Z=(Z_t)_{t\geq 0}$$ is an arbitrary non-negative non-decreasing non-anticipating process, right-continuous for $$t>0$$.
The stochastic analysis technique is somewhat different on the recent papers of Radner and Shepp.
Reviewer: P.Stavre (Craiova)

MSC:
 91B82 Statistical methods; economic indices and measures 91B60 Trade models