L3

I will start the talk by discussing renormlisation group in perturbative algebraic quantum field theory (pAQFT) and its non-perturbative incarnation acting on the Buchholz-Fredenhagen dynamical C*-algebra. I will also explain how pAQFT can be used to derive functional renormlisation group (FRG) equations that generalize Wetterich equations to globally hyperbolic Lorentzian manifolds and arbitrary states (beyond the usual FRG in the vacuum).

TBA

TBA

We propose a novel Black-Scholes model under which the stock price processes are modeled by stochastic differential equations driven  by sub-diffusions. The new framework can capture the less financial activity phenomenon during the bear markets while having the classical Black-Scholes model as its special case. The sub-diffusive spot market is arbitrage-free but is in general incomplete. We investigate the pricing for European-style contingent claims under this new model. For this, we study the Girsanov transform for sub-diffusions and use it to find risk-neutral probability measures for the new Black-Scholes model. Finally, we derive the explicit formula for the price of European call options and show that it can be determined by a partial differential equation (PDE) involving a fractional derivative in time, which we coin a time-fractional Black-Scholes PDE.