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January to February 2018 From 23 to 25 January 2018, RMI hosted three consecutive pedagogical lectures by Prof. Halil Soner or ETH Zurich. This series of lectures titled, “Hedging-Pricing Duality” considered a more general financial market with Knightian uncertainty. Prof. Soner explained that although in such markets - by definition - there is no historical measure, the basic duality between hedging and pricing still holds. His lectures, which are based on his research, illustrated this connection by several convex duality results starting with simple discrete time models. From 12 to 14 February 2018, Prof. Masaaki Kijima of Tokyo Metropolitan University hosted three pedagogical lectures on “An Expansion Approach for the Pricing of Exotic Options.” According to his current research, the talks presented a proposal of approximation method based on chaos expansion for pricing of European-style contingent claims, how to apply this method for the pricing of exotic options such as reciprocal options, volume-weighted-average-price (VWAP) options, and barrier options, and lastly he also considered a fractional volatility model and elaborated on how the expansion approach could be applied. The third set of three-day pedagogical lectures was hosted by Prof. Nizar Touzi of Ecole Polytechnique. In the lecture series titled, “Continuous-Time Principal-Agent Problem,” Prof. Touzi stated that the Principal-Agent problem is the cornerstone for the modeling of optimal incentive schemes to account for moral hazard in economics and shared his research methodology for solving Stackelberg game problems in continuous time setting.
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