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- W2971001748 abstract "In this paper we continue investigating the optimal dividend and investment problems under the Sparre Andersen model. More precisely, we assume that the claim frequency is a renewal process instead of a standard compound Poisson process, whence semi-Markovian. Building on our previous work cite{BaiMa17}, where we established the dynamic programming principle via a {it backward Markovization} procedure and proved that the value function is the unique {it constrained} viscosity solution of the HJB equation, in this paper we focus on the construction of the optimal strategy. The main difficulties in this effort is two fold: the regularity of the viscosity solution to a non-local, nonlinear, and degenerate parabolic PDE on an unbounded domain, which seems to be new in its own right; and the well-posedness of the closed-loop stochastic system. By introducing an auxiliary PDE, we construct an $e$-optimal strategy, and prove the well-posedness of the corresponding closed-loop system, via a bootstrap technique with the help of a Krylov estimate." @default.
- W2971001748 created "2019-09-05" @default.
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- W2971001748 date "2019-08-30" @default.
- W2971001748 modified "2023-09-27" @default.
- W2971001748 title "On Optimal Dividend and Investment Strategy under Renewal Risk Models" @default.
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