Previous work has shown that unobservable random shocks on output have a detrimental effect on efficiency in short-term (‘static’) employment relationships. Given the prevalence of long-term (‘dynamic’) relationships in firms, we investigate whether the impact of shocks is similarly pronounced in gift-exchange relationships where the same principal-agent pair interacts repeatedly. In dynamic relationships, shocks have a significantly less pronounced negative effect on efficiency than in static relationships. In an attempt to identify the drivers for our results we find that the combination of a repeated-game effect (current misbehavior can be punished in future periods) and a noise-canceling effect (part of the noise cancels out in the long run) is required to avoid the detrimental effects of unobservable random shocks on efficiency.

This paper proposes a shift in the valuation and production of long-term annuities, away from the classical risk-neutral methodology towards a methodology using the real-world probability measure. The proposed production method is applied to three examples of annuity products, one having annual payments linked to a mortality index and the savings account and the others having annual payments linked to a mortality index and an equity index with a guarantee that is linked to the same mortality index and the savings account. Out-of-sample hedge simulations demonstrate the effectiveness of the proposed less-expensive production method. In contrast to classical risk-neutral production, which revolves around the savings account as reference unit, the long-term best-performing portfolio, the numéraire portfolio of the equity market, is employed as the fundamental reference unit in the production of the annuity. The numéraire portfolio is the strictly positive, tradable portfolio that when used as denominator or benchmark makes all benchmarked non-negative portfolios supermartingales. Under real-world valuation, the initial benchmarked value of a benchmarked contingent claim equals its real-world conditional expectation. The proposed real-world valuation and production can lead to significantly lower values of long-term annuities and their less-expensive production than suggested by the risk-neutral approach.

In this paper, I analyze an optimal loan contract between a risk-neutral financial intermediary and a risk-averse household, where the household receives a stochastic endowment stream that grows over time and is unable to commit to the contract. I examine the household's welfare in the equilibrium contract, and find that, first, under sufficiently rapid endowment growth, the presence of uncertainty in endowment may improve the household's welfare through relaxation of its commitment problem, and second, regardless of the endowment growth rate, the household's welfare is nonincreasing in the persistence of endowment. Numerical analysis suggests that welfare improvement from uncertainty may occur under reasonable parameters. These results have potentially important practical implications—for example, for developing countries that rely on external borrowing.