A gap between rational annuitization price for producer and price for customer

The paper studies pricing of insurance products focusing on the pricing of annuities under uncertainty. This pricing problem is crucial for financial decision making and was studied intensively; however, many open questions still remain. In particular, there is a so-called ``annuity puzzle" related to certain inconsistency of existing financial theory with the empirical observations for the annuities market. The paper suggests a pricing method based on the risk minimization such that both producer and customer seek to minimize the mean square hedging error accepted as a measure of risk. This leads to two different versions of the pricing problem: the selection of the annuity price given the rate of regular payments, and the selection of the rate of payments given the annuity price. It appears that solutions of these two problems are different. This can contribute to explanation for the "annuity puzzle"

On the implied market price of risk under the stochastic numéraire

This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. An equivalent martingale measure is not unique for this market, and there are non-replicable claims. Some rational choices of the equivalent martingale measures are suggested and discussed, including implied measures calculated from bond prices constructed as a risk-free investment with deterministic payoff at the terminal time. This leads to possibility to infer a implied market price of risk process from observed historical bond prices