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Shafer and Vovk introduce in their book Game-theoretic foundations for probability and finance the notion of instant enforcement. In this paper we introduce an outer measure on the space of continuous paths which assigns zero value exactly to those sets (properties) of pairs of time $t$ and elementary event $omega$ which are instantly blockable. Next, for the introduced measure we prove BDG inequalities and use them to define It^o-type integral. Additionally, we prove few properties for the quadratic variation of model-free continuous paths which hold with instant enforcement.
We consider a 2-dimensional marked Hawkes process with increasing baseline intensity in order to model prices on electricity intraday markets. This model allows to represent different empirical facts such as increasing market activity, random jump si
In a discrete-time financial market, a generalized duality is established for model-free superhedging, given marginal distributions of the underlying asset. Contrary to prior studies, we do not require contingent claims to be upper semicontinuous, al
In this paper, we are concerned with the valuation of Guaranteed Annuity Options (GAOs) under the most generalised modelling framework where both interest and mortality rates are stochastic and correlated. Pricing these type of options in the correla
We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually he
We test the price momentum effect in the Korean stock markets under the momentum universe shrinkage to subuniverses of the KOSPI 200. Performance of the momentum strategy is not homogeneous with respect to change of the momentum universe. It is found