Conference Agenda

We prove a version of the fundamental theorem of asset pricing~(FTAP) in continuous time that is based on the strict no-arbitrage condition and that is applicable to both frictionless markets and markets with proportional transaction costs. We consider a market with a single risky asset whose ask price process is higher than or equal to its bid price process. Neither the concatenation property of the set of wealth processes, that is used in the proof of the frictionless FTAP, nor some boundedness property of the trading volume of admissible strategies usually argued with in models with a nonvanishing bid-ask spread need to be satisfied in our model.

\url{https://arxiv.org/abs/2307.00571}

We are interested in the absence of arbitrage for single asset financial market models whose asset price process is modeled by a one-dimensional general regular diffusion (captured via scale function and speed measure). In recent work, Criens and Urusov proved precise characterizations of NA, NUPBR and NFLVR in terms of scale and speed. In particular, it was shown that these notions are violated in the presence of skewness effects or reflecting boundaries (that reflection entails such arbitrage opportunities is rather intuitive). It remained open whether weaker notions of no arbitrage can hold in the presence of skewness or reflection. The literature suggests that this is not the case. Indeed, Rossello (Insur. Math. Econ., 2012) had observed that the weaker "no increasing profit" (NIP) condition fails for an exponential skew Brownian motion model, and Buckner, Dowd and Hulley (Finance & Stochastics, 2024) showed that increasing profits exist in a reflected geometric Brownian motion model. In this talk, we explain the surprising observation that there are diffusion markets that satisfy NIP in the presence of skewness effects and reflecting boundaries.

We revisit the classical problem of equilibrium asset pricing in a continuous-time complete-market setting, but in the case where investors' preferences are described by Epstein-Zin Stochastic Differential Utility. The market is comprised of a riskless bond and a risky asset, where the latter pays continuously a stochastic dividend stream. The equilibrium is characterised by a system of strongly coupled Forward-Backward Stochastic Differential Equations (FBSDEs). This is joint work in progress with Dr. Martin Herdegen.

We revisit the classical topic of mean-variance equilibria in the setting of continuous time, where asset prices are driven by continuous semimartingales. We show that under mild assumptions, a mean-variance equilibrium corresponds to a quadratic equilibrium for different preference parameters. We then use this connection to study a fixed-point problem that establishes existence of mean-variance equilibria. Our results rely on fine properties of mean-variance hedging as well as a novel stability result for quadratic BSDEs. The talk is based on joint work with Christoph Czichowsky, Martin Herdegen and David Martins.