This dissertation consists of two essays on contract theory. I investigate contracts under different economics contexts. In the first chapter, I consider a two-period model in which the success of the firm depends on the effort of a first-period manager (the incumbent) and the ability of a second-period manager. At the end of the first period, the board receives a noisy signal of the incumbent manager's ability and decides whether to retain or replace the incumbent manager. I show that the information technology the board has to assess the incumbent manager's ability is an important determinant of the optimal contract and replacement policy. The contract must balance providing incentives for the incumbent manager to exert effort and ensuring that the second-period manager is of high ability. I show that severance pay in the contract serves as a costly commitment device to induce effort. Unlike existing models, I identify conditions on the information structure under which both entrenchment and anti-entrenchment emerge in the optimal contract. In the second chapter, I use a dynamic model of life insurance with one-sided commitment and bequest-driven lapsation, as in Daily, Hendel and Lizzeri (2008) and Fang and Kung (2010), but with policyholders who may underestimate the probability of losing their bequest motive, to analyze how the life settlement market -- the secondary market for life insurance -- may affect consumer welfare in equilibrium. I show that life settlement may increase consumer welfare in equilibrium when (i) policyholders are sufficiently overconfident; and (ii) the intertemporal elasticity of substitution of consumption (IES) of policyholders is greater than one.