Let F be a distribution function supported on (-∞,∞) with a finite mean μ. In this note we show that if its tail F = 1 - F is dominatedly varying, then for any r > max{μ, 0}, there exist C(r) > 0 and D(r) &g...Let F be a distribution function supported on (-∞,∞) with a finite mean μ. In this note we show that if its tail F = 1 - F is dominatedly varying, then for any r > max{μ, 0}, there exist C(r) > 0 and D(r) > 0 such thatfor all n ≥ 1 and all x≥rn. This inequality sharpens a classical inequality for the subexponential distribution case.展开更多
The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan introduced the notion of allowable strategy and showed that condition of NFLVR w...The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan introduced the notion of allowable strategy and showed that condition of NFLVR w.r.t. allowable strategies is independent of the choice of numeraire and is equivalent to the existence of an equivalent martingale measure for the deflated price process. In this paper we establish a version of the Kramkov's optional decomposition theorem in the setting of equivalent martingale measures. Based on this theorem, we have a new look at some basic concepts in arbitrage pricing theory: superhedging, fair price,attainable contingent claims, complete markets and etc.展开更多
Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal wit...Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal with the ess. inf case, the transplantation of results to the ess. sup case being trivial.展开更多
基金Yan's work was supported by the Ministry of Science and Technology of China (973 Project on Mathematics) the Knowledge Innovation Program of the Chinese Academy of Sciences.
文摘Let F be a distribution function supported on (-∞,∞) with a finite mean μ. In this note we show that if its tail F = 1 - F is dominatedly varying, then for any r > max{μ, 0}, there exist C(r) > 0 and D(r) > 0 such thatfor all n ≥ 1 and all x≥rn. This inequality sharpens a classical inequality for the subexponential distribution case.
基金The work of Yan was supported by the National Natural Science Foundation of China, grant 79790130and the 973 project on forward problems of mathematics at the core, the Ministry of Science and Technology.
基金The main results of this paper were reported in ref. [6]without giving the proofs.
文摘The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan introduced the notion of allowable strategy and showed that condition of NFLVR w.r.t. allowable strategies is independent of the choice of numeraire and is equivalent to the existence of an equivalent martingale measure for the deflated price process. In this paper we establish a version of the Kramkov's optional decomposition theorem in the setting of equivalent martingale measures. Based on this theorem, we have a new look at some basic concepts in arbitrage pricing theory: superhedging, fair price,attainable contingent claims, complete markets and etc.
文摘Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal with the ess. inf case, the transplantation of results to the ess. sup case being trivial.
