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The devastating consequences of tsunamis on coastal infrastructure have highlighted the urgent need for effective disaster risk reduction strategies. To mitigate tsunami disasters, the insurance industry plays a vital role in implementing risk transfer measures by providing financial protection against asset damage. However, the current research on catastrophe insurance policies for coastal infrastructure lacks consideration of climate change effects. It is essential to take into account the non-stationary effects of sea-level rise to develop long-term tsunami disaster mitigation measures and promote socioeconomic resilience in coastal communities. This paper aims to provide an insurance portfolio optimization framework for coastal residential buildings subjected to tsunamis considering non-stationary sea-level rise effects based on a stochastic simulation approach. A spatiotemporal probabilistic sea-level rise hazard assessment is carried out by utilizing available climate models and considering several emission scenarios. Tsunami propagation analyses under various sea-level rise cases are performed to evaluate the time-variant tsunami hazard curves based on Monte Carlo simulation. A life cycle-based stochastic insurance claim model associated with the cumulative loss of building assets is developed based on a non-stationary compound renewal process. Finally, a sample average approximation method is leveraged to estimate the optimum basic insurance premium rate by maximizing the insurer's profit under a cost-constrained insurance purchase decision of homeowners. As a case study, the proposed framework is applied to multiple municipalities situated in the tsunami-prone region of Kochi Prefecture, Japan. Sea-level rise substantially decreases the maximum profits of tsunami insurers and increases the premium rate and ruin probability. [ABSTRACT FROM AUTHOR]