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April 17th, 2002, 4:31 am
Forum: Numerical Methods Forum
Topic: Quasi Monte Carlo : On Dimensionality
Replies: 42
Views: 178600

Quasi Monte Carlo : On Dimensionality

<t>Very basic question:Do I understand the application of quasirandom numbers correctly as follows:Suppose that we have to evaluate the path t\in[0,T]->S(t) of an asset S at the points 0=t0<t1<...<tn=T and let us writeS=(S(t0),S(t1),...,S(tn)) for this path. The path is driven by a sequence z0,z1,.....
April 17th, 2002, 12:01 am
Forum: Technical Forum
Topic: Stochastic Integral for Finance
Replies: 21
Views: 191952

Stochastic Integral for Finance

<t>Pat,Suppose we trade without restrictions (ie. not selffinancing) on [0,T] with weights H(t) investing in assets S(t). The value V(t) of the position at time tis given by V(t)=H(t).S(t) (dot product). If the strategy is not selffinancing the change in value V(T)-V(0)=H(T).S(T)-H(0).S(0)is almost ...
April 5th, 2002, 6:36 pm
Forum: Technical Forum
Topic: Stochastic Integral for Finance
Replies: 21
Views: 191952

Stochastic Integral for Finance

<t>Let h be the option payoff at time T, C(t) the discounted option price at time t, H(t) the replicating strategy and S(t) the discounted asset vector (a risk neutral martingale), V(t)=H(t).C(t) the portfolio price at time t and<br/> <br/> G(t)=integral_0^t H(u)dS(u) <br/> <br/> the gains from trad...
April 5th, 2002, 1:28 pm
Forum: Technical Forum
Topic: Stochastic Integral for Finance
Replies: 21
Views: 191952

Stochastic Integral for Finance

<t>Selffinancing condition: every stratey can be made selffinancing by suitably altering the weight of just one asset (raise needed funds from short sale, store superfluous funds by going long the asset).<br/> <br/> Thus the selffinancing condition is not really that fundamental.<br/> In fact you ca...
April 5th, 2002, 1:11 pm
Forum: Technical Forum
Topic: Stochastic Integral for Finance
Replies: 21
Views: 191952

Stochastic Integral for Finance

<t>"If the payoff h=h(S(T)) can be replicated by a sellfinancing strategy then h=h(s) must be homogenous of degree one in s"<br/> <br/> I have seen this statement in a serious paper (FINASTO) however it is obviously false.<br/> <br/> The simplest Black-Scholes market is known to be COMPLETE and henc...
April 4th, 2002, 2:59 pm
Forum: Technical Forum
Topic: Markov and Martingale
Replies: 12
Views: 190246

Markov and Martingale

You missed that part of the definition of "Markov" which expresses the fact that conditioning at time t is equivalent to restarting the process at time 0 in the state of time t.

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