Such advantages would include the fact that the insurer will be able to sell nonparticipating insurance
products freely, a move partially restricted while it remains a mutual insurance company under insurance laws, he said.
The stock company, on the other hand, can issue both participating and nonparticipating insurance contracts, and sets premiums on all policies to provide stockholders with a fair expected return.
In other words, policyholders with low levels of risk aversion will tend to associate with participating mutual contracts, while those with high levels of risk aversion will desire partially or nonparticipating insurance. The intuitive reason for this is straightforward: participating in aggregate (risky) profits exposes an insured to additional risk, and will be chosen only by those most willing to bear such risk.
Section 2 develops a basic model of nonparticipating insurance where stockholders use a multivariate contingent claims framework to set premiums that produce a fair expected return.
The "policyholder-choice problem" of choosing the optimal level of nonparticipating insurance coverage is well understood in the context of both nonparticipating (Borch, 1968 and Arrow, 1974) and participating contracts (Doherty, 1991; Doherty and Dionne, 1993; Smith and Stutzer, 1995).
If losses can be decomposed into two additive components, one independent among insureds and the other highly correlated, then variable participation contracts can be replicated through the combination of a traditional nonparticipating insurance policy and a futures contract to hedge the systemic risk component.
Whether the optimal contract is achieved via nonparticipating insurance with insureds hedging the [epsilon] risk directly in the futures market or via variable participation contracts with insurer-based securitization is likely to depend upon which method is more cost-effective once transaction costs are introduced.
From the insurer's perspective, the ex ante risk per policyowner under full nonparticipating insurance is (essentially) [xi]EL [equivalent to] [p.sub.0]EL(1 + [epsilon]).
If individuals must insure the noncorrelated (idiosyncratic) component of their loss exposure through a nonparticipating insurance contract, then securitized products may develop to allow the individual to directly hedge the correlated (systemic) risk component.
In the first stage, the firm decides to issue either participating or nonparticipating insurance
policies, and it receives some proceeds from the policyholders.
Table 1 Summary Statistics on Participating Insurance Policies, 1991: Stock and Mutual Life/Health Insurers Variable Stock Number of Firms with Participating Insurance in Force 475 Participating Insurance in Force (in thousands) $737,702,461 Nonparticipating Insurance in Force (in thousands) $5,182,287,977 Participating Insurance in Force (percent) 12.5 Nonparticipating Insurance in Force (percent) 87.5 Variable Mutual Number of Firms with Participating Insurance in Force 109 Participating Insurance in Force (in thousands) $4,158,552,512 Nonparticipating Insurance in Force (in thousands) $255,179,094 Participating Insurance in Force (percent) 94.2 Nonparticipating Insurance in Force (percent) 5.8
Since [V.sub.1] - [V.sub.2] [is greater than] 0, we know that there exists an [L.sup.*] such that [S.sub.1] - [S.sub.2] = 0 for nonparticipating insurance contracts (i.e., where [Gamma] = 0), and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for [Gamma] = 0 and L [is less than] [L.sup.*].