Module Specifications..
Current Academic Year 2024  2025
Please note that this information is subject to change.
 
None 

Description This postgraduate course covers asset pricing, with emphasis on a rigorous analysis of continuoustime models. Arbitrage, trading strategies, market completeness. Portfolio choice in complete and incomplete markets. Myopic and hedging demand. Derivatives pricing: riskneutral pricing and risk premia.  
Learning Outcomes 1. Prove the main results in Mathematical Finance 2. Solve portfolio choice problems rigorously 3. Price assets and derivatives with advanced models 4. Design hedging strategies for new financial products 5. Develop customized pricing methods 6. Critically evaluate the assumptions underlying different asset pricing models  
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml 

Indicative Content and Learning Activities
Arbitrage Assets, Payoffs, Simple and Gross Returns, Strategies, Selffinancing portfolios, Arbitrage, Stochastic Discount Factors, First and Second Fundamental Theorems of Asset Pricing, Law of one price. Hedging Hedging Arbitrage bounds, Replication Bounds, Superhedging, Superreplication Theorem, Market Completeness, Perfect Replication, Redundancy of Assets. Optimality Utility Functions, Absolute and Relative Risk Aversion, Allais and Ellsberg paradoxes, Savage Representation, Arbitrage and Utility, Firstorder condition, Investment and Consumption. Logarithmic, Power, and Exponential Utilities. MeanVariance Analysis Expected Return and Risk, State PriceBeta Representation, HansenJagannathan Bound, MeanVariance Frontier, Twofund Separation Duality Legendre Transforms and their properties, Duality Method for Verification, Pricing by Marginal Utility. Duality Bounds. Continuous Time Bachelier and Samuelson models. Continuous trading. Doubling strategies. Admissible Strategies. Local Martingales and Supermartingales. No arbitrage and Admissibility. Stochastic Discount Factors and Martingale Measures. Bayes' formula. Diffusion Models Instantaneous returns and covariances. Stochastic exponential. Discount factors in diffusion models and risk premia. Representation of payoffs. Portfolio Choice Utility maximization from terminal wealth and consumption. Solution by Duality in Bachelier and Samuelson models with exponential and power utility. Merton and Markowitz formulas. General solution in complete markets. Duality with consumption. Stochastic Control Dynamic programming. Value Function. HamiltonJacobiBellman equations. Verification. Homogeneity. Stochastic Investment Opportunities. Asset Prices and State Variables. Incompleteness. Intertemporal Hedging. Logarithmic and Power Transformations. Longrun limits. Martingale Measures and RiskNeutral Dynamics. Longrun optimality. Finitehorizon Bounds.  
 
Indicative Reading List
 
Other Resources None  
Programme or List of Programmes
 
Archives: 
