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Erscheinungsjahr: 
2021
Quellenangabe: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 9 [Issue:] 1 [Article No.:] 17 [Publisher:] MDPI [Place:] Basel [Year:] 2021 [Pages:] 1-18
Verlag: 
MDPI, Basel
Zusammenfassung: 
Consider an insurance company whose surplus is modelled by an arithmetic Brownian motion of not necessarily positive drift. Additionally, the insurer has the possibility to invest in a stock modelled by a geometric Brownian motion independent of the surplus. Our key variable is the (absolute) drawdown Δ of the surplus X, defined as the distance to its running maximum ¯X. Large, long-lasting drawdowns are unfavourable for the insurance company. We consider the stochastic optimisation problem of minimising the expected time that the drawdown is larger than a positive critical value (weighted by a discounting factor) under investment. A fixed-point argument is used to show that the value function is the unique solution to the Hamilton-Jacobi-Bellman equation related to the problem. It turns out that the optimal investment strategy is given by a piecewise monotone and continuously differentiable function of the current drawdown. Several numerical examples illustrate our findings.
Schlagwörter: 
drawdown
optimal investment
stochastic control
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