quadratic twists of elliptic curves in this paper we give the method of constructing non torsion points on elliptic curves which generalizes the classical birch lemma as an application we get more quadratic twist families of the elliptic curve x 0 49 which have rank one this report is a combination of the two joint works coates li tian zhai proc lond math soc 110 2 357 394 2015 4 cai li wang sci china math 59 7 1307 1326 2016 2

can one make any crash prediction in finance using the local hurst exponent idea abstract we apply the hurst exponent idea for investigation of djia index time series data the behavior of the local hurst exponent prior to drastic changes in financial series signal is analyzed the optimal length of the time window over which this exponent can be calculated in order to make some meaningful predictions is discussed our prediction hypothesis is verified with examples of 1929 and 1987 crashes as well as with more recent phenomena in stock market from the period 1995 to 2003 some interesting agreements are found

the pricing of european options on two underlying assets with delays abstract in the paper the pricing of european options on two underlying assets with delays is discussed by using the approach of equivalent martingale measure transformation the market is proved to be complete with exchange option as a particular example we obtain the explicit pricing formula in a subinterval of option period the robust euler maruyama method is combined with the monte carlo simulation to compute exchange option prices within the whole option period numerical experiments indicate that there is an increasing possibility of the difference between the delayed and black scholes option prices with the increase of delay

forecasting volatility of fuel oil futures in china garch type sv or realized volatility models abstract in most previous works on forecasting oil market volatility squared daily returns were taken as the proxy of unobserved actual volatility however as demonstrated by andersen and bollerslev 1998 22 this proxy with too high measurement noise could be perfectly outperformed by a so called realized volatility rv measure calculated by the cumulative sum of squared intraday returns with this motivation we further extend earlier works by employing intraday high frequency data to compare the performance of three typical volatility models in the daily out of sample volatility forecasting of fuel oil futures on the shanghai futures exchange shfe the garch type stochastic volatility sv and realized volatility models by taking rv as the proxy of actual daily volatility and then computing forecasting errors we find that the realized volatility model based on intraday high frequency data produces significantly more accurate volatility forecasts than the garch type and sv models based on daily returns furthermore the sv model outperforms many linear and nonlinear garch type models that capture long memory volatility and or the asymmetric leverage effect in volatility these results also prove that abundant volatility information is available in intraday high frequency data and can be used to construct more accurate oil volatility forecasting models

derived heights and generalized mazur tate regulators 2 algebraic preliminaries 4 2 1 notations and conventions 4 2 2 duality 5 2 2 1 local duality 5 2 2 2 global duality 6 2 3 assumptions 8 2 4 preliminary calculations 10

arithmetic of formal groups and applications i universal norm subgroups the theory of the norm map for the formal multiplicative group is well known as local class field theory in 1972 mazur 14 in his generalization of iwasawa theory to abelian varieties over number fields made quite clear that it is absolutely crucial for such a global theory first to understand the norm map for the formal groups attached to abelian varieties he achieved this understanding in case of formal groups of multiplicative type by using the theory of proalgebraic groups later on lubin and rosen 12 gave a completely elementary approach to mazur s results in the meantime hazewinkel 8 had settled the case of one dimensional commutative formal lie groups his method consists in an explicit and very complicated study of the properties of the power series coefficients of the logarithm of a formal group law by means of higher ramification theory in the same spirit vvedenskij 18 and konovalov 10 reproved and slightly extended hazewinkel s results let k q be a finite extension with ring of integers r and residue class field and koo k be a ramified zv extension with ring of integers r and f gal koo k let i r denote a smooth connected commutative formal r group of finite dimension d i e a commutative formal lie group if k k is the intermediate layer of degree p in koo k r its ring of integers and g gal k k its galois group then we know from the description of ff as a formal lie group that

on the boundary behavior of kahler einstein metrics on log canonical pairs in this paper we study the boundary behavior of the negatively curved kahler einstein metric attached to a log canonical pair x d such that k x d is ample in the case where x is smooth and d has simple normal crossings support but possibly negative coefficients we provide a very precise estimate on the potential of the ke metric near the boundary d in the more general singular case d being assumed effective though we show that the ke metric has mixed cone and cusp singularities near d on the snc locus of the pair as a corollary we derive the behavior in codimension one of the ke metric of a stable variety

on the p adic height of heegner cycles 0 1 in gr za gross and zagier proved a remarkable formula which relates the first derivative of the l function of a modular form f of weight 2 on 0 n over a suitable imaginary quadratic field and the neron tate height of a heegner point over the same quadratic field on the f part of the jacobian of the modular curve x0 n later perrin riou pr 2 proved a p adic version of this formula kolyvagin s method of euler systems ko combined with the formula of gross zagier proves the conjecture of birch and swinnerton dyer up to a controlled rational factor for all modular elliptic curves over q with analytic rank 1

cube sum problem and an explicit gross zagier formula a nonzero rational number is called a it cube sum if it is of the form a 3 b 3 with a b in bbb q times in this paper we prove that for any odd integer k geq 1 there exist infinitely many cube free odd integers n with exactly k distinct prime factors such that 2n is a cube sum resp not a cube sum we present also a general construction of heegner points and obtain an explicit gross zagier formula which is used to prove the birch and swinnerton dyer conjecture for certain elliptic curves related to the cube sum problem

generalized heegner cycles and p adic rankin l series this article studies a distinguished collection of so called generalized heegner cycles in the product of a kuga sato variety with a power of a cm elliptic curve its main result is a p adic analogue of the gross zagier formula which relates the images of generalized heegner cycles under the p adic abel jacobi map to the special values of certain p adic rankin l series at critical points that lie outside their range of classical interpolation

a delay financial model with stochastic volatility martingale method abstract in this paper we extend a delayed geometric brownian model by adding a stochastic volatility term which is driven by a hidden process of fast mean reverting diffusion to the delayed model combining a martingale approach and an asymptotic method we develop a theory for option pricing under this hybrid model the core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term subsequently a correction effect on the european option price is demonstrated both theoretically and numerically for a good agreement with practical results

the p adic gross zagier formula for elliptic curves at supersingular primes let p be a prime number and let e be an elliptic curve defined over of conductor n let k be an imaginary quadratic field with discriminant prime to pn such that all prime factors of n split in k b perrin riou established the p adic gross zagier formula that relates the first derivative of the p adic l function of e over k to the p adic height of the heegner point for k when e has good ordinary reduction at p in this article we prove the p adic gross zagier formula of e for the cyclotomic p extension at good supersingular prime p our result has an application for the full birch and swinnerton dyer conjecture suppose that the analytic rank of e over is 1 and assume that the iwasawa main conjecture is true for all good primes and the p adic height pairing is not identically equal to zero for all good ordinary primes then our result implies the full birch and swinnerton dyer conjecture up to bad primes in particular if e has complex multiplication and of analytic rank 1 the full birch and swinnerton dyer conjecture is true up to a power of bad primes and 2

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

exceptional zero formulae and a conjecture of perrin riou let a mathbf q be an elliptic curve with split multiplicative reduction at a prime p we prove an analogue of a conjecture of perrin riou relating p adic beilinson kato elements to heegner points in a mathbf q and a large part of the rank one case of the mazur tate teitelbaum exceptional zero conjecture for the cyclotomic p adic l function of a more generally let f be the weight two newform associated with a let f infty be the hida family of f and let l p f infty k s be the mazur kitagawa two variable p adic l function attached to f infty we prove a p adic gross zagier formula expressing the quadratic term of the taylor expansion of l p f infty k s at k s 2 1 as a non zero rational multiple of the extended height weight of a heegner point in a mathbf q