stochastic calculus.pdf - Stochastic Calculus for Finance...

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Stochastic Calculus for Finance Albert Cohen Actuarial Sciences Program Department of Mathematics Department of Statistics and Probability A336 Wells Hall Michigan State University East Lansing MI 48823 [email protected] [email protected] Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 1 / 249
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Course Information Syllabus to be posted on class page in first week of classes Homework assignments will posted there as well Page can be found at Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 2 / 249
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Course Information Many examples within these slides are used with kind permission of Prof. Dmitry Kramkov, Dept. of Mathematics, Carnegie Mellon University. Course Textbook: Stochastic Calculus for Finance (Springer Finance.) Some examples here will be similar to those practice questions publicly released by the SOA. Please note the SOA owns the copyright to these questions. This book will be our reference, and some questions for assignments will be chosen from it. Copyright for all questions used from this book belongs to Springer. From time to time, we will also follow the format of Marcel Finan’s A Discussion of Financial Economics in Actuarial Models: A Preparation for the Actuarial Exam MFE/3F. Some proofs from there will be referenced as well. Please find these notes here Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 3 / 249
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What are financial securities? Traded Securities - price given by market. For example: Stocks Commodities Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 4 / 249
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What are financial securities? Traded Securities - price given by market. For example: Stocks Commodities Non-Traded Securities - price remains to be computed. Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 4 / 249
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What are financial securities? Traded Securities - price given by market. For example: Stocks Commodities Non-Traded Securities - price remains to be computed. Is this always true? Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 4 / 249
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What are financial securities? Traded Securities - price given by market. For example: Stocks Commodities Non-Traded Securities - price remains to be computed. Is this always true? We will focus on pricing non-traded securities. Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 4 / 249
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How does one fairly price non-traded securities? Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 5 / 249
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How does one fairly price non-traded securities? By eliminating all unfair prices Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 5 / 249
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How does one fairly price non-traded securities? By eliminating all unfair prices Unfair prices arise from Arbitrage Strategies Start with zero capital End with non-zero wealth Albert Cohen (MSU) STT 888: Stochastic Calculus for Finance MSU 2016 5 / 249
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How does one fairly price non-traded securities?
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