This paper studies modelling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for...

This paper studies modelling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account and a family of European options for all maturities with a fixed payoff function h. We first characterize absence of arbitrage in...

In this work, we investigate SDEs whose coefficients may depend on the entire past of the solution process. We introduce different Lipschitztype conditions on the coefficients. It turns out that for existence and uniqueness of a strong solution it suffices to have Lipschitz continuity in mean,...

<Para ID="Par1">This paper explores, in a multiperiod setting, the funding liquidity of a borrower that finances its operations through short-term debt. The short-term debt is provided by a continuum of creditors with heterogeneous beliefs about the prospects of the borrower. In each period, creditors observe...</para>

In this work, we investigate SDEs whose coefficients may depend on the entire past of the solution process. We introduce different Lipschitz-type conditions on the coefficients. It turns out that for existence and uniqueness of a strong solution it suffices to have Lipschitz continuity in mean,...

We analyze mean-variance-optimal dynamic hedging strategies in oil futures for oil producers and consumers. In a model for the oil spot and futures market with Gaussian convenience yield curves and a stochastic market price of risk, we find analytical solutions for the optimal trading...