Learning goals:

After successfully attending this lecture, many common methods for determining prices and portfolio models in finance will be understood. The focus is not just on finance alone, but also on the theory behind it.

Contents:

The course will provide rigorous yet focused training in stochastic calculus and mathematical finance. Topics to be covered:

1. Stochastic Calculus: Stochastic Processes, Brownian Motion and Martingales, Entropy, Stopping Times, Local martingales, Doob-Meyer Decomposition, Quadratic Variation, Stochastic Integration, Ito Formula, Girsanov Theorem, Jump-diffusion Processes, Stable and Levy processes.
    
2. Mathematical Finance: Pricing Models, The Black-Scholes Model, State prices and Equivalent Martingale Measure, Complete Markets and Redundant Security Prices, Arbitrage Pricing with Dividends, Term-Structure Models (One Factor Models, Cox-Ingersoll-Ross Model, Affine Models), Term-Structure Derivatives and Hedging, Mortgage-Backed Securities, Derivative Assets (Forward Prices, Future Contracts, American Options, Look-back Options), Incomplete Markets, Markets with Transaction Costs, Optimal Portfolio and Consumption  Choice (Stochastic Control and Merton continuous time optimization  problem, CAPM), Equilibrium models, Numerical Methods.

Workload:

Total effort with 4.5 credit points: approx. 135 hours

Attendance time: 30 hours Preparation/follow-up: 65 hours

Exam and exam preparation: 40 hours

literature references

• Dynamic Asset Pricing Theory, Third Edition by D. Duffie, Princeton University Press, 1996
• Stochastic Calculus for Finance II: Continuous-Time Models by S. E. Shreve, Springer, 2003
• Stochastic Finance: An Introduction in Discrete Time by H. Föllmer, A. Schied, de Gruyter, 2011
• Methods of Mathematical Finance by I. Karatzas, S. E. Shreve, Springer, 1998
• Markets with Transaction Costs by Yu. Kabanov, M. Safarian, Springer, 2010
• Introduction to Stochastic Calculus Applied to Finance by D.Lamberton, B. Lapeyre, Chapman&Hall,1996
• Statistisches und machinelles Lernen, S.Richter, Springer, 2019

Block Event

Schedule and Location:

Thu. 09.11.2023  room 212, building 8.30 -

time 09:30 - 17:00

Fri. 10.11.2023  room 212, building 8.30 -

time 09:30 - 17:00

Wed. 22.11.2023  room 001, building 40.28 -

time 14:00 - 18:00

Thu. 23.11.2023  room 110, building 40.50 -

time 09:30 - 17:00

Wed. 17.01.2024  room 001, building 40.28 -

time 09:30 - 17:00

Thu. 18.01.2024  room 604, building10.50 -

time 09:30 - 17:00

Wed. 24.01.24  room 001, building 40.28 -

time 09:30 - 17:00

Thu. 25.01.2024  room 110, building 40.50 -

time 09:30 - 17:00

Wed. 14.02.2024  seminar room Forum A + B, building 3.95 -

time 09:30 - 17:00

Thu. 15.02.2024  seminar room Forum A + B, building 3.95 -

time 09:30 - 17:00