Robust Equilibrium Yield Curves

This paper studies the quantitative implications of the interaction between robust control and stochastic volatility for key asset pricing phenomena. We present an equilibrium term structure model with a representative agent and an output growth process that is conditionally heteroskedastic. The agent does not know the true model of the economy and chooses optimal policies that are robust to model misspecification. The choice of robust policies greatly amplifies the effect of conditional heteroskedasticity in consumption growth, improving the model’s ability to explain asset prices. In a robust control framework, stochastic volatility in consumption growth generates both a state-dependent market price of model uncertainty and a stochastic market price of risk. We estimate the model using data from the bond and equity markets, as well as consumption data. We show that the model is consistent with key empirical regularities that characterize the bond and equity markets. We also characterize empirically the set of models the robust representative agent entertains, and show that this set is ?small?. That is, it is statistically difficult to distinguish between models in this set.Yield curves, Market price of Uncertainty, Robust control.

An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility

We are concerned with an investment and consumption problem with stochastic interest rate and stochastic volatility, in which interest rate dynamic is described by the Cox-Ingersoll-Ross (CIR) model and the volatility of the stock is driven by Heston’s stochastic volatility model. We apply stochastic optimal control theory to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function and choose power utility and logarithm utility for our analysis. By using separate variable approach and variable change technique, we obtain the closed-form expressions of the optimal investment and consumption strategy. A numerical example is given to illustrate our results and to analyze the effect of market parameters on the optimal investment and consumption strategies

Robust Equilibrium Yield Curves

This paper studies the quantitative implications of the interaction between robust control and stochastic volatility for key asset pricing phenomena. We present an equilibrium term structure model in which output growth is conditionally heteroskedastic. The agent does not know the true model of the economy and chooses optimal policies that are robust to model misspecification. The choice of robust policies greatly amplifies the effect of conditional heteroskedasticity in consumption growth, improving the model's ability to explain asset prices. In a robust control framework, stochastic volatility in consumption growth generates both a state-dependent market price of model uncertainty and a stochastic market price of risk. We estimate the model using data from the bond and equity market, as well as consumtion data. We show that the model is consistent with key empirical regularities that characterize the bond and equity markets. We also characterize empirically the set of models the robust representative agent entertains, and show that this set is "small". In other words, it is statistically difficult to distinguish between models in this set.Yield curve, market price of uncertainty, robust control

Inventories and Optimal Monetary Policy

We introduce inventories into a standard New Keynesian Dynamic Stochastic General Equilibrium (DSGE) model to study the effect on the design of optimal monetary policy. The possibility of inventory investment changes the transmission mechanism in the model by decoupling production from final consumption. This allows for a higher degree of consumption smoothing since firms can add excess production to their inventory holdings. We consider both Ramsey optimal monetary policy and a monetary policy that maximizes consumer welfare over a set of simple interest rate feedback rules. We find that in contrast to a model without inventories, Ramsey-optimal monetary policy in a model with inventories deviates from complete inflation stabilization. In the standard model, nominal price rigidity is a deadweight loss on the economy, which an optimizing policymaker attempts to remove. With inventories, a planner can reduce consumption volatility and raise welfare by accumulating inventories and letting prices change as an equilibrating mechanism. We find also find that the application of simple rules comes very close to replicating Ramsey optimal outcomes.Ramsey policy, New Keynesian model

Risk, productive government expenditure, and the world economy

This paper analyzes the expenditure policy of the public sector and risk in a two-country stochastic AK growth model, provided that public spending is productivity- and volatility-enhancing. First we derive the world macroeconomic equilibrium. Then we study the impact of changes in exogenous variables on consumption, growth, and welfare. Next, we show that consumption-wealth ratio and welfare should be higher in an open economy than in a closed economy. We discuss whether open economies grow more than closed economies. Then the optimal size of the public sector is derived in two different scenarios in an open economy. We get that the size of the public sector which maximizes welfare is lower than that which maximizes growth. Finally, we analyze whether more open economies are associated with a higher optimal size of the public sector. The optimal size in an open economy can be higher than that in a closed economy for two reasons: different marginal impact of public spending on productivity and risk diversification.risk, productive government expenditure, consumption, growth, welfare, optimal size of the public sector

Essays in Financial and Insurance Mathematics.

This dissertation consists of the following three parts: (i) We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset. The price of the risky asset is assumed to follow a diffusion with stochastic volatility. Given the rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability of outliving the wealth. Techniques from stochastic optimal control are used. (ii) We extend the Heston stochastic volatility model to include state-dependent jumps in the price and the volatility, and develop a method for the exact simulation of this model. The jumps arrive with a stochastic intensity that may depend on time, price, volatility and jump counts. The jumps may have an impact on the price or the volatility, or both. The random jump size may depend on the price and volatility. The exact simulation method is based on projection and point process filtering arguments. Numerical experiments illustrate the features of the exact method. (iii) We study the properties of sovereign credit risk using Credit Default Swap (CDS) spreads for U.S. and major sovereign countries. We develop a regime-switching two-factor model that allows for both global-systemic and sovereign-specific credit shocks, and use maximum likelihood estimation to calibrate model parameters to weekly CDS data. The preliminary results suggest that there is heterogeneity across different countries with respect to their sensitivity to system risk. Furthermore, the high-volatility and low-volatility regimes behave differently with asymmetric regime-shift probabilities.Ph.D.Applied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91381/1/xyhu_1.pd

Optimal funding and investment strategies in defined contribution pension plans under Epstein-Zin utility

A defined contribution pension plan allows consumption to be redistributed from the plan member’s working life to retirement in a manner that is consistent with the member’s personal preferences. The plan’s optimal funding and investment strategies therefore depend on the desired pattern of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution, and we also take into account the member’s human capital. We show that a stochastic lifestyling approach, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches is an optimal investment strategy. In addition, the optimal contribution rate each year is not constant over the life of the plan but reflects trade-offs between the desire for current consumption, bequest and retirement savings motives at different stages in the life cycle, changes in human capital over the life cycle, and attitude to risk