On the cost‐of‐capital rate under incomplete market valuation

Abstract

In this paper we discuss the concept of the cost-of-capital rate for an insurance company as an equilibrium in the economic triangle of policyholders, shareholders and the regulator. This provides a possible rationalization and an economic foundation for a quantity that is widely used in practice but whose value is typically neither technically nor economically well justified. We show how it can be well-founded in such a triangular equilibrium. Under a simple one-period model and a valuation procedure of a two-price economy for illiquid assets we provide a corresponding economic-theoretical quantification for the cost-of-capital rate. The resulting rates are illustrated by a number of concrete numerical examples.

Approximations of multi-period liability values by simple formulas

“…It can be argued that the capital provider, seen as the share holder of the company, has limited liability and is not required to continue injecting capital if the the value R t of available asset turns out insufficient to match the value X t+1 + V t+1 of the liability towards the policy holders. For discussions on limited liability in the context of cost-ofcapital valuation we refer to Albrecher et al [1] and Möhr [9]. In the setting with limited liability, (7)…”

Insurance–finance arbitrage

“…Since long, the insurance industry has gone further, beginning with BEL (but without clear mention of the probability being used) and adding RM, solvency capital, and so forth. In complementing our work, we shall introduce the objectives of shareholders, insurance seekers, and the regulator (see Albrecher et al., 2022). From this point of view, we shall look at industry's linear best estimates, regulatory RM and capital requirement.…”