August 3rd, 2002, 9:13 pm
QuoteOriginally posted by: rezanot sure if I understand wellif x=M(s,t)dx = [ dM/dt + dM/ds f(s) + 1/2 d2M/ds2 g2(s) ] dt + dM/ds g(s) dW so I guess we need to get fromdx=m(s,x) dtsomething likedx = h(s,t) dt + n(s,t) dWand identify the two equations above ...do you have the actual expression for dx=m(s,x) dt ?is there a way to get something like dx = h(s,t) dt + n(s,t) dW ???Cheers for the response Reza.To fill in some of the blanks, the problem comes from a stochastic DP.There's an underlying price, S, that satisfies some kind of stochastic process.Also, there's the state of the system, x, (the details of what the system actuallyis aren't really relevant to this bit of the calculation). After calculating the DP, you get a policy function, that defines how you change the state with each combination of price and system state.Hence the equation, dx=m(s,x)dt, where m is the policy function.I suppose I could write the equations asds=f(s)dt+g(s)dW1dx=m(s,x)dt+dum.dW2where dum is a dummy volatility number then construct a 2D Kolmogorov equation in (s,x), solve this, then integrate over s to get the density in x. Then finally takethe limit dum->0. However I strongly suspect the limits won't exist. cheers,Tom