We focus on the asymptotic convergence behavior of the hedging errors of European stock option due to discrete hedging under stochastic interest rates. There are two kinds of BS-type discrete hedging differ in hedging...We focus on the asymptotic convergence behavior of the hedging errors of European stock option due to discrete hedging under stochastic interest rates. There are two kinds of BS-type discrete hedging differ in hedging instruments: one is the portfolio of underlying stock, zero coupon bond, and the money market account (Strategy BSI); the other is the underlying stock, zero coupon bond (Strategy BSII). Similar to the results of the deterministic interest rate case, we show that convergence speed of the discounted hedging errors is 1/2-order of trading frequency for both strategies. Then, we prove each of the BS-type strategy is not only locally optimal, but also globally optimal under the corresponding measure. Finally, we give some numerical examples to illustrate the results. All the discussion is based on non-arbitrage condition and zero transaction cost.展开更多
For a class of manufacturing systems with homogeneous Markov machine failure rates,the stationary probability distribution of the part surplus can be calculated for given tentative values of hedging points. Some prope...For a class of manufacturing systems with homogeneous Markov machine failure rates,the stationary probability distribution of the part surplus can be calculated for given tentative values of hedging points. Some properties on the ordering of optimal hedging points are obtained.展开更多
Background:The allocation of resources between offspring size and number is a central question of life-history theory.Although several studies have tested the existence of this trade-off,few studies have investigated ...Background:The allocation of resources between offspring size and number is a central question of life-history theory.Although several studies have tested the existence of this trade-off,few studies have investigated how environmental variation influences the allocation of resources to offspring size and offspring number.Additionally,the relationship between population dynamics and the offspring size and number allocation is far less understood.Methods:We investigate whether resource allocation between egg size and clutch size is influenced by the ambient temperature and whether it may be related to apparent nest survival rate.We measured 1548 eggs from 541 nests of two closely related shorebird species,the Kentish Plover(Charadrius alexandrinus)and the White-faced Plover(C.dealbatus)in China,in four populations that exhibit contrasting ambient environments.We weighed females,monitored nest survival,and calculated the variance of ambient temperature.Results:Although we found that egg size and clutch size were all different between the four breeding populations,the reproductive investment(i.e.total clutch volume)was similar between populations.We also found that populations with a high survival rate had relatively larger eggs and a smaller clutch than populations with a low nest survival rate.The latter result is in line with a conservative/diversified bet-hedging strategy.Conclusions:Our findings suggest that plovers may increasing fitness by investing fewer,larger or many,small according local nest survival rate to make a similar investment in reproduction,and thereby may have an impact on population demography.展开更多
In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging e...In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.展开更多
The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modu...The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, the drift and the volatility of the exchange rate dynamics all depend on a continuous-time hidden Markov chain which can be interpreted as the states of a macro-economy. In this paper, we will provide a practical lognormal diffusion dynamic of the spot foreign exchange rate for market practitioners. We employing the minimal martingale measure to demonstrate a system of coupled partial-differential-integral equations satisfied by the currency option price and attain the corresponding hedging schemes and the residual risk. Numerical simulations of the double exponential jump diffusion regime-switching model are used to illustrate the different effects of the various parameters on currency option prices.展开更多
基金supported by National Basic Research Program of China (Grant No.2007CB814905)
文摘We focus on the asymptotic convergence behavior of the hedging errors of European stock option due to discrete hedging under stochastic interest rates. There are two kinds of BS-type discrete hedging differ in hedging instruments: one is the portfolio of underlying stock, zero coupon bond, and the money market account (Strategy BSI); the other is the underlying stock, zero coupon bond (Strategy BSII). Similar to the results of the deterministic interest rate case, we show that convergence speed of the discounted hedging errors is 1/2-order of trading frequency for both strategies. Then, we prove each of the BS-type strategy is not only locally optimal, but also globally optimal under the corresponding measure. Finally, we give some numerical examples to illustrate the results. All the discussion is based on non-arbitrage condition and zero transaction cost.
文摘For a class of manufacturing systems with homogeneous Markov machine failure rates,the stationary probability distribution of the part surplus can be calculated for given tentative values of hedging points. Some properties on the ordering of optimal hedging points are obtained.
基金This work was supported by Open Fund of Key Laboratory of Biodiversity Science and Ecological Engineering,Ministry of Education to Yang Liu,the China Postdoctoral Science Foundation(No.2019M663221)the British Ornithologists’Union’s Career Development Bursary in 2019 to Zitan Song,the National Natural Science Foundation of China(Nos.31600297)to Pinjia Queby the Hungarian Scientific Funding Agency,NKFIH(éLVONAL KKP-126949,K-116310)to Tamás Székely.
文摘Background:The allocation of resources between offspring size and number is a central question of life-history theory.Although several studies have tested the existence of this trade-off,few studies have investigated how environmental variation influences the allocation of resources to offspring size and offspring number.Additionally,the relationship between population dynamics and the offspring size and number allocation is far less understood.Methods:We investigate whether resource allocation between egg size and clutch size is influenced by the ambient temperature and whether it may be related to apparent nest survival rate.We measured 1548 eggs from 541 nests of two closely related shorebird species,the Kentish Plover(Charadrius alexandrinus)and the White-faced Plover(C.dealbatus)in China,in four populations that exhibit contrasting ambient environments.We weighed females,monitored nest survival,and calculated the variance of ambient temperature.Results:Although we found that egg size and clutch size were all different between the four breeding populations,the reproductive investment(i.e.total clutch volume)was similar between populations.We also found that populations with a high survival rate had relatively larger eggs and a smaller clutch than populations with a low nest survival rate.The latter result is in line with a conservative/diversified bet-hedging strategy.Conclusions:Our findings suggest that plovers may increasing fitness by investing fewer,larger or many,small according local nest survival rate to make a similar investment in reproduction,and thereby may have an impact on population demography.
基金Supported by the National Natural Science Foundation of China(11671115)the Natural Science Foundation of Zhejiang Province(LY14A010025)
文摘In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.
基金Supported by the National Natural Science Foundation of China(No.11301454,No.71771147 and No.71201100)the Jiangsu Qing Lan Project for Excellent Young Teachers in University(2014)+1 种基金Six Talent Peaks Project in Jiangsu Province(2016-JY-081)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17KJB110020)
文摘The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, the drift and the volatility of the exchange rate dynamics all depend on a continuous-time hidden Markov chain which can be interpreted as the states of a macro-economy. In this paper, we will provide a practical lognormal diffusion dynamic of the spot foreign exchange rate for market practitioners. We employing the minimal martingale measure to demonstrate a system of coupled partial-differential-integral equations satisfied by the currency option price and attain the corresponding hedging schemes and the residual risk. Numerical simulations of the double exponential jump diffusion regime-switching model are used to illustrate the different effects of the various parameters on currency option prices.
