The value of a liability cash flow in discrete time subject to capital requirements

TL;DR

This paper develops a market-consistent valuation method for insurance liabilities in discrete time, considering repeated capital requirements and optimal stopping, aligning with regulatory standards.

Contribution

It introduces a novel valuation framework based on hypothetical transfers and optimal stopping, incorporating capital requirements into multi-period liability valuation.

Findings

Defines the liability value as a no-arbitrage price considering capital requirements.

Formulates the valuation as a sequence of coupled optimal stopping problems.

Provides a backward recursion method for computing the liability value.

Abstract

The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the approach presented is based on a hypothetical transfer of the original liability and a replicating portfolio to an empty corporate entity whose owner must comply with repeated one-period capital requirements but has the option to terminate the ownership at any time. The value of the liability is defined as the no-arbitrage price of the cash flow to the policyholders, optimally stopped from the owner's perspective, taking capital requirements into account. The value is computed as the solution to a sequence of coupled optimal stopping problems or, equivalently, as the solution to a backward recursion.