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<p>The drawdown of a stochastic process is the absolute distance to its historical peak. It is a widely used risk and performance measure in financial applications. For a diffusion process subject to a continuous-time control process, we consider a stochastic control problem targeting the simultaneous maximisation of growth of the running maximum and minimisation of the weighted occupation time in the area bounded away from it by at least <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(d&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. The model we consider corresponds to a diffusion risk model under proportional reinsurance. The optimal reinsurance strategies obtained lead to a stabilisation of this surplus process close to its own running maximum. In particular, they promote growth of the surplus while simultaneously avoiding large negative deviations from the current record high. By exploiting connections to Hamilton–Jacobi–Bellman-equations and reflected SDEs, we find explicit expressions for the value functions and strategies and show that the processes under the optimal feedback controls exist. We discuss examples and implications of our results in the context of the application.</p>

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Stabilised surplus and profits through reinsurance based on drawdown optimisation

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Leonie Violetta Brinker,
  • Hanspeter Schmidli

摘要

The drawdown of a stochastic process is the absolute distance to its historical peak. It is a widely used risk and performance measure in financial applications. For a diffusion process subject to a continuous-time control process, we consider a stochastic control problem targeting the simultaneous maximisation of growth of the running maximum and minimisation of the weighted occupation time in the area bounded away from it by at least \(d>0\) d > 0 . The model we consider corresponds to a diffusion risk model under proportional reinsurance. The optimal reinsurance strategies obtained lead to a stabilisation of this surplus process close to its own running maximum. In particular, they promote growth of the surplus while simultaneously avoiding large negative deviations from the current record high. By exploiting connections to Hamilton–Jacobi–Bellman-equations and reflected SDEs, we find explicit expressions for the value functions and strategies and show that the processes under the optimal feedback controls exist. We discuss examples and implications of our results in the context of the application.