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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
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