We introduce uncertainty into the Holmstrom and Milgrom (1987) model to study optimal long-term contracting with learning. In the dynamic relationship, the agent's shirking not only reduces the current output, but also increases the agent's information rent due to the persistent belief manipulation e¤ect. We characterize the optimal contract by solving a dynamic programming problem in which information rent is the unique state variable. We …nd that in the optimal contract, the optimal e¤ort decreases stochastically over time, exhibiting a front-loaded pattern. Furthermore, the optimal contract exhibits an option-like feature in that incentives increase after good performance.
Value-at-risk (VaR) and expected shortfall (ES) are now both widely used risk measures. However, users have not paid much attention to the estimation risk issues, especially in the case of heteroskedastic financial time series. The key challenge arises from the fact that the estimated generalized autoregressive conditional heteroskedasticity (GARCH) innovations are not the true independent innovations. The purpose of this work is to provide an analytical method to assess the precision of conditional VaR and ES in the GARCH model estimated by the filtered historical simulation (FHS) method based on the asymptotic behavior of the residual empirical distribution function in GARCH processes. The proposed method is evaluated by simulation and proved valid.
Distinguishing between adverse selection and moral hazard is a difficult but important issue in insurance economics. In the present work, we model and evaluate the distinct roles of adverse selection, ex ante moral hazard, and ex post moral hazard in China's automobile insurance market. Our econometric analysis supports the following conclusions: (1) the effect of asymmetric information on the probability of claims is significant; (2) the effect of ex ante moral hazard on the probability of claims is not significant, establishing adverse selection as the underlying source of information asymmetry; (3) the effect of asymmetric information (including ex ante moral hazard) on the severity of claims is not significant; and (4) the impact of ex post moral hazard on claim severity is significant for a subset of lower‐coverage policyholders. Consequently, it may be advisable for Chinese automobile insurance companies to allocate greater resources to both underwriting (i.e., selecting policyholders) and auditing claims.
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