Stochastic Riesz spaces with applications in theoretical finance

International audience ; In this paper, we develop a theory of stochastic Riesz spaces equipped with a stochastic topology that allows to define a general financial market model defined by a partial order. For such a model, we provide a construction of continuous-time portfolio processes from the discrete-time ones. We study the no-arbitrage condition AIP of the literature that states that the super-hedging prices of the non negative European claims are non negative. We show that this condition may be equivalent in discrete-time and in continuous-time and that the infimum super-hedging prices of a given payoff may also coincide in discrete-time and in continuous-time. At last, the construction of an upper linear stochastic integral is proposed in the setting of stochastic Riesz spaces.