In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company's surplus process is assumed to follow a Brownian motion with drift, and the reinsurance...

We show how to solve Merton optimal investment stochastic control problem for Hawkesbased models in finance and insurance (Propositions 1 and 2), i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t)...

In this paper we present a methodology of model-based calibration of additional capital needed in an interconnected financial system to minimize potential contagion losses. Building on ideas from combinatorial optimization tailored to controlling contagion in case of complete information about...

In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company's surplus process is assumed to follow a Brownian motion with drift, and the reinsurance...

Due to recent technical progress, battery energy storages are becoming a viable option in the power sector. Their optimal operational management focuses on load shift and shaving of price spikes. However, this requires optimally responding to electricity demand, intermittent generation, and...

This paper presents a unified theory of human capital with both health capital and, what we term, skill capital endogenously determined within the model. By considering joint investment in health capital and in skill capital, the model highlights similarities and differences in these two...

We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to Γ-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under the semigroup. To overcome this issue, we consider different...

We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g. because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible...

Land subsidence threatens the living conditions of roughly 1.2 billion people worldwide in deltaic regions characterized by soft top soil. Economic activity in deltaic regions requires lowering the groundwater levels to keep the land sufficiently dry to maintain productivity, which, however,...

We develop a flexible single-state model to represent tradeoffs between infections and activity during the early phase of an epidemic. We prove that optimal policy is continuous in the state but discontinuous in the deterministic arrival date of a cure; optimal lockdowns are followed by stimulus...