On Pricing Analysis In A Discrete-time Market With Random Interval Payoffs

This paper was concerned a composite and financial market model, influenced by random and interval. In the market, the security payoffs was described by random interval. Random interval not only reflects the uncertainty of future market state, but also covers the possible range of the security price under each future state. A pricing analysis model was established in the discrete-time market with random interval payoffs.Paper was first studied the contingent claim pricing problems with stochastic in-terval payoffs in the single-period market. A strong arbitrage and on-arbitrage concept was discussed in the discrete-time market and on-arbitrage pricing rules in classic mar-ket were promoted by strong no-arbitrage pricing rules adapted to the random interval market. We proved the equivalence between on-existence of strong arbitrage and ex-istence of risk-neutral pricing measure by the proof method of fundamental pricing theorem in the classic market. The contingent claim pricing problems was discussed under the on-arbitrage conditions in the extend market. This price rang can be ex-pressed by the payoffs of contingent claim and the risk-neutral pricing measure.Paper was also studied the pricing in the multi-market of discrete-time. The multi-market was separated into many structures in the single market. The strong on-arbitrage of multi-market attributed to the single market. In order to get the equivalent description of strong on-arbitrage in the multi-market, the single market of current price and the contingent claim with random interval. The strong no-arbitrage existence of the single market with current price was equal with the existence of risk-neutral pricing measure. Security price represented the conditional expectation of future payoffs in the risk-neutral pricing measure. In limited state and interval market with random interval was equal with the existence of multi-market in the risk-neutral pricing measure. In this measure, securities price in any mid-time can be expressed as conditional expectation of final payoffs in the risk-neutral pricing measure.At the same time, the worst value process of security was super-martingale and the best value process was latter-martingale. The contingent claim pricing was also expounded in the multi-market.The random interval market with payoffs was promoted by random interval mar-ket. No-arbitrage analysis builded a general foundation of payoffs in the random inter-val market and also established basis on the financial market promoting to the more complex uncertain market.