**Mathematics A (Autumn Semester)**

**Assessment Program, University of St. Gallen**

Mathematical logic, sequences, series, financial mathematics, functions, inverse functions, logarithm, exponential, properties of continuous functions, properties of differentiable functions, marginal functions, elasticity, growth rate, differential, extreme points, Taylor polynomials, functions of two variables, contour lines, partial derivatives, partial elasticities, total differential, implicit function theorem, homogeneous functions, production functions and homogeneity.

Further information at http://studynet.unisg.ch

**Mathematics B (Spring Semester)**

**Assessment Program, University of St. Gallen**

Optimisation of functions with two variables, with and without constraints, integration, applications of the integral, matrices, vectors, linear dependence and independence, rank of a matrix, systems of linear equations, Cramer’s rule, Gauss algorithm, eigenvalues, eigenvectors, linear difference equations of order 1.

Further information at http://studynet.unisg.ch

**Mathematics (Autumn Semester)**

**Master Program in Economics, University of St. Gallen**

Nonlinear optimization with constraints and applications, implicit function theorem, envelope theorem, convex analysis (Kuhn-Tucker Theorem), dynamic optimization and applications, selected topics in measure theory, selected topics in probability theory.

Further information at http://studynet.unisg.ch

**Advanced Mathematics (Spring Semester)**

**Master Program in Quantitative Economics and Finance, University of St. Gallen**

The course introduces stochastic calculus and some of its applications in Finance. We first define basic concepts in probability theory, as filtered probability spaces, conditional expectations and martingales. We then define the stochastic integral for simple processes first and for general processes then. We present three crucial results in stochastic calculus – the Ito Lemma, the Girsanov Theorem and the Martingale Representation Theorem, – and discuss their relevance for Finance.The lectures combine theoretical parts with exercises (four exercise series will be distributed and discussed during the sessions).

Further information at http://studynet.unisg.ch

**Quantitative Risk Management**

**Master Program in Quantitative Economics and Finance, University of St. Gallen**

The global financial crises that erupted in 2008 has intensified the interest in risk management among financial institutions. It is now generally recognized that poor risk management has been one of the causes of the financial crises. In particular, credit risk and operational risk, the first being the risk that a counterparty in a financial contract might fail to fulfill its contractual obligations, the second being the risk of losses due to management failures or inadequate systems, are not well understood. The course focuses on quantitative models for assessing credit and operational risk. We first introduce the notations of risk factors and risk measures. We then discuss the two main approaches for modeling credit risk. Finally, we study extreme value theory, that deals with extreme events (as big losses due to management failures), and apply it to assess operational risk.

Further information at http://studynet.unisg.ch

**Mathematical Methods in Finance (Spring Semester)**

**PhD Program in Quantitative Economics and Finance, University of St. Gallen**

The course covers topics in dynamic portfolio selection and asset pricing in a continuous-time setting. The final goal is to study mathematical techniques from stochastic calculus and their application in finance.

Further information at http://studynet.unisg.ch