Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market

Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation

“…We later specify the specific (second order) criteria for our solution for both types of equilibrium. We next quote from Asmussen et al (2019) some results that will allow replacing optimization problems in the space of functions p 1 , p 2 by the more elementary problem of pointwise maximization/minimization of the real-valued ratio…”

“…The analysis is based on the diffusion approximation to a standard Cramér-Lundberg risk process, extended to allow investment in a risk-free asset. In Asmussen et al (2019), this idea is extended to a situation where insurance companies compete against each other, and Nash equilibria in premium controls of the resulting stochastic differential game are determined under suitable conditions. However, in some cases, no Nash equilibrium exists.…”

“…Two insurance companies compete against each other such that one company is the leader, choosing its premium first, and the other company is the follower, choosing its premium in response to the leader's. The setting is slightly modified relative to that in Asmussen et al (2019), in that we do not consider search and switching costs when modelling the customer's choice between insurance products. Our main contributions are, first, to establish the existence of Stackelberg equilibrium under suitable conditions on this strategic game between insurance companies, and to identify the restrictions under which this reduces to the special case of Nash equilibrium.…”

“…Stackelberg-type equilibria of stochastic differential games have been studied in Lin et al (2012), where an insurance company selects an investment strategy while the market (or nature) selects a worst-case probability scenario, and in Chen and Shen (2018), where the game is between insurer and reinsurer, but not as here in a game between insurance companies. For some more remote references, see Asmussen et al (2019). Stackelberg games were introduced by von Stackelberg (1934), and the theory of stochastic differential Stackelberg games is considered by Yong (2002), Bensoussan et al (2015), and Shi et al (2016).…”

“…Information frictions have been modelled as differences in the cost of obtaining information, e.g., by Salop and Stiglitz (1977). In Asmussen et al (2019) we study premium competition between insurance companies in the presence of market frictions. In the present paper, we consider instead product differentiation, and for simplicity abstract from market frictions.…”