Title Page -- Preface -- Contents -- Part 1. Real Options -- Optimal Investment Under Liquidity Constraints -- Introduction -- Optimal Investment in Perfect Capital Markets -- The Benchmark Model -- Discussion -- Optimal Stopping for a Cash-Constrained Firm -- The Model -- Value of the Firm with No Growth Option -- Value of the Firm with a Growth Option -- A Verification Theorem -- Solution to Optimal Stopping Problem Fi -- Fi as a Super Solution to HJB Equation (3.13) -- Future Works -- Investment in High-Tech Industries: An Example from the LCD Industry -- Introduction -- The Investment Model with Geometric Brownian Motion -- Investment in LCD Industry -- Industry -- Production Process -- Data and Estimations -- Industry Analysis -- Conclusion -- Appendix -- Proof of Proposition 1 -- Proof of Proposition 2 -- Game Theoretic Real Options and Competition Risk -- Introduction -- General Set-Up of a Real Option Duopoly -- Preemption Games -- Markov Perfect Equilibrium -- Firm Value and Welfare Implications -- Conclusion -- Real Options and Risk Aversion -- Introduction -- Model and Assumptions -- Real Options and Investment Timing -- The Benchmark Case: Risk Neutrality -- Investment Timing and Risk Aversion -- Model Implications -- Risk Aversion and the Option Value to Wait -- Risk Aversion and Project Value -- Probability of Investment -- Conclusion -- Appendix -- A General Result -- Proofs -- Real Options with Time and Scale Flexibility -- Introduction -- Flexibility in Time and Scale -- Optimal Investment Strategy -- Capital Accumulation Rule -- Optimal Investment Timing -- Specific Examples in Real Options Analysis -- Example 1: Linear Revenue -- Example 2: Cobb-Douglas Production Function -- Example 3: Bounded Production -- Conclusion -- Appendices -- Appendix A -- Appendix B -- Appendix C -- Part 2. Ambiguity.

Optimal Stopping Rule Meets Ambiguity -- Introduction -- Optimal Stopping Under Ambiguity -- Discrete Time Framework -- Finite Time Horizon -- Infinite Time Horizon -- Continuous Time Framework -- Aggregator and Examples -- Value Process Under Ambiguity -- Infinite Time Horizon -- Comparative Analysis -- Ambiguity and Optimal Rule -- Risk Aversion -- Markov Setting -- Value function in Ambiguity -- Comments and Extensions -- Ambiguity and Ambiguity Aversion -- Optimal Stopping Under Risk Measures -- Conclusion -- Appendix A: Optimal Stopping Related to Reflected BSDEs -- Finite Time Horizon -- Infinite Time Horizon -- Appendix B: Proofs of Results on the Problem of Optimal Stopping -- Appendix C: Proof of Results in Extensions -- An Overview on the Principal-Agent Problems in Continuous Time -- Introduction -- Principal-Agent Problems Under Full Information -- Principal-Agent Problems with Hidden Actions and Lump-Sum Payment -- Principal-Agent Problems with Hidden Actions and Continuous Payment -- Optimal Insurance Design Problem Under Knightian Uncertainty -- Ambiguity Setting -- Pareto-Efficient Insurance Design -- Optimal Insurance Design from the Insured's Perspective -- Pareto-Optimal Insurance Contract -- Conclusion -- Nonlinear Expectation Theory and Stochastic Calculus Under Knightian Uncertainty -- Introduction -- BSDE and g-Expectation -- Recall: SDE and Related Ito's Stochastic Calculus -- BSDE: Existence, Uniqueness and Comparison Theorem -- Nonlinear g-Expectation Through BSDE -- g-Expectation and g-Martingales -- Inverse Problem: Is an Expectation E a g-Expectation? -- BSDE Applied in Finance -- Nonlinear Expectations and Nonlinear Distributions -- Expectation Space (Omega, H, E) -- Distributions and Independence -- Central Limit Theorem and Law of Large Numbers -- Normal Distributions Under a Sublinear Expectation.

Central Limit Theorem and Law of Large Numbers -- Sample Based Sublinear Expectations -- Brownian Motion Under a Sublinear Expectation -- Brownian Motion Under a Sublinear Expectation -- Construction of a G-Brownian Motion -- G-Brownian Motion in a Complete Sublinear Expectation Space -- L^p_G (Omega) is a Subspace of Measurable Functions on Omega -- Ito Integral of G-Brownian Motion -- Quadratic Variation Process of G-Brownian Motion -- Ito's Formula for G-Brownian Motion -- Stochastic Differential Equations -- Brownian Motions, Martingales Under Nonlinear Expectation -- Applications to Finance -- Part 3. Risk and Insurance -- Proportional Mutual Reinsurance Optimization -- Introduction -- The Model -- Feasible Control -- Cost Structure and Value Function -- Variational Inequalities for the Optimal Value Function -- Solution of the QVI -- The HJB Equation in the Continuation Region -- A Solution to the Auxiliary Problem -- The Optimal Value Function for the Original Problem -- The case of K^+ \leq K^+ -- The case of K^+ > K^+ -- Verification Theorem and the Optimal Control -- Conclusions -- Downside Risk Minimization: Large Deviation Estimates for Controlled Semimartingales -- Introduction -- Related H-J-B Equations -- Problems on a Finite Time Horizon -- Large Time Asymptotics -- Differentiability of H-J-B Equation -- The Equivalent Stochastic Differential Game -- Duality Theorem -- On Dynamic Portfolio Insurance Techniques -- Introduction -- Market Model -- A Generalized CPPI -- Generalized Drawdown Constraint -- American OBPI and DFP -- American OBPI Method -- DFP Method -- Long-Term Risk-Sensitized Growth-Rate Maximization -- Long-Term Optimality with Floor Constraint -- Long-Term Optimality with Generalized Drawdown Constraint -- Credit Risk Models: A Review -- Introduction -- Structural Models -- Merton model -- Longstaff and Schwartz Model.

Leland, and Leland and Toft Models -- Collin-Dufresne and Goldstein Model -- Chen, Collin-Dufresne and Goldstein Model -- Reduced Forms -- Empirical Analysis-Structural Models -- Conclusion -- Author Index.