Abstract. We study zero-sum optimal stopping games (Dynkin games) between two players who disagree about the underlying model. In a Markovian setting, a verification result is established showing that if a pair of functions can be found that satisfies some natural conditions, then a Nash equilibrium of stopping times is obtained, with the given functions as the corresponding value functions. In general, however, there is no uniqueness of Nash equilibria, and different equilibria give rise to different value functions. As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times.

We consider a financial market with a savings account and a stock S that follows a general diffusion. The default of the company, which issues the stock S, is modeled as a stopping time with respect to the filtration generated by the value of the firm that is not observable by regular investors. We assume that the stock price and the value of the firm are correlated. We study three investors with different information levels trading in the market who aim to price a general default-sensitive contingent claim. We use the density approach and Yor's method to solve the pricing problem. Specifically, we find the sets of equivalent martingale measures in three cases and, when needed, we choose one of them using f -divergence approach.

Credit Value Adjustment (CVA) is the difference between the value of the default-free and credit-risky derivative portfolio, which can be regarded as the cost of the credit hedge. Default probabilities are therefore needed, as input parameters to the valuation. When liquid CDS are available, then implied probabilities of default can be derived and used. However, in small markets, like the Nordic region of Europe, there are practically no CDS to use. We study the following problem: given that no liquid contracts written on the default event are available, choose a model for the default time and estimate the model parameters. We use the minimum variance hedge to show that we should use the real-world probabilities, first in a discrete time setting and later in the continuous time setting. We also argue that this approach should fulfil the requirements of IFRS 13, which means it could be used in accounting as well. We also present a method that can be used to estimate the real-world probabilities of default, making maximal use of market information (IFRS requirement).