The Company's Investment Behavior And Principal-agent Relationship Under The Condition Of Model Uncertainty

Models that involve uncertainty typically assume that uncertainty parameters should take the familiar form of risk(i.e.,a probability measure).Consequently,in continuous-time applications,the dynamics of a risky variable(such as the cash flows of a project)are often described by some known stochastic processes such as Brownian motion.However,uncertainty is a rich and complex concept that may not be limited to risk.Thus,in this dissertation,we distinguish ambiguity/model uncertainty from risk and set up formal model of mathematical finance,in which we solve the optimal contracting problem or/and firm value maximization by corporate investment,pay-performance sensitivity,consumption dynamics and capacity choice.The contributions of the dissertation are summed up as follows:(1)Despite its central role in contract theory,evidence on trade-off between risk and incentives remains inconclusive.We revisit this trade-off by incorporating model uncertainty and costly hedging.Principals who face model uncertainty endogenously induce pessimism towards future prospects and consequently desire ambiguity sharing by offering higher managerial incentives.Conventionally,higher exposure to business risk,similar to costlier hedging,requires higher risk compensation which,in turn,lowers the incentive provision.Concern for model mis-specification distorts this effect in that higher risk exposure deteriorates the ambiguity induced pessimism which naturally leads to higher incentives.Moreover,the dominance of these two opposing effect largely depends on hedging costs,because higher hedging costs reinforce the latter effect.In contrast to the standard negative linkage on risk-incentive trade-off,the ambiguity sharing motive under costly hedging can rationalize positive,negative as well as irrelevant relationship between idiosyncratic business risk and incentives.Furthermore,the influence mechanism of ambiguity to incentive coefficient and the effort level is analyzed on the second best and first best occasion.The conclusion is different to the existing studies which assume that the principal and the agent are rational.In the presence of model uncertainty,the incentive to the agent is still needed in the optimal contract and from the perspective of ambiguity-averse principal,model mis-specification mitigates the moral hazard problem.(2)We consider a robust contract with limited commitment in continuous time.First,we find the existence of limited commitment attenuates the negative effect of model uncertainty on the principal’s value.In addition,concerns regarding model mis-specification motivate the principal to increase the agent’s exposure to income risk,which increases the sensitivity of certainty equivalent wealth with respect to an income shock.Furthermore,our theoretical model predicts that limited commitment makes the ambiguity averse principal less pessimistic.When there is only limited commitment or model uncertainty,the growth rate and volatility of the agent’s consumption are constant.Interestingly,when there exist both ingredients,the growth rate and volatility of consumption become state dependent and increasing in the agent’s promised utility.Finally,when there exist both limited commitment and model uncertainty,the growth rate and volatility of wage become state dependent and the wage dynamics exhibit both right skewness and decreases as the empirical data.(3)We extend dynamic agency and investment theory by incorporating model uncertainty.As concerns regarding model uncertainty induce a trade-off between incentives and ambiguity sharing,the principal tends to delay the cash payout to the agent.We find model uncertainty lowers the firm value,the average q and marginal q,where q is defined as the ratio between a physical asset’s market value and its replacement value.Furthermore,model uncertainty leads to insufficient investment,which provides an alternative explanation for under-investment.Finally,the optimal pay-performance sensitivity of the agent’s continuation value to the firm’s output is state dependent and exceeds the lower bound when it is close to the payout boundary.(4)We present a principal-agent model integrating ambiguity and real option.A risk-averse manager can exert costly hidden effort to increase productivity growth of a firm.In addition,the ambiguity-averse owners of the firm can irreversibly increase the firm capital stock.The quantitative analysis exhibits that model uncertainty may accelerate investment,raise the optimal effort policy and increase the pay-performance sensitivity.(5)We introduce Knightian uncertainty into the standard model of capacity choice and investigates its impact on the firm’s expansion decision.First,we find Knightian uncertainty reduces both the firm value and marginal value of capital.Under Knightian uncertainty,the firm’s expansion decision is shown to be more conservative.When the firm value is decomposed into the value of assets in place and growth opportunities,we find the value reduction caused by Knightian uncertainty is much more substantial for the value of growth opportunities.For asset returns,our model provides an alternative explanation for the cross-sectional dispersion in beta from the perspective of behavior economics.Specifically,we show that the existence of ambiguity lowers the beta of the firm through the channel of growth opportunities since the beta of assets in place is not affected by model uncertainty.Finally,the implications of the user cost of capital and stationary distribution of firm value are also examined.