I am starting a new job with a energy company. Within the division I will work at, I will be running models that help calculate the most effective way to inject and extract gas from the storage facilities they own. Although I do not need to know all the mathematics behind the model, I want to make the right impression and learn some things on my own. I have did some reserach and found a paper that does the very samething i like. But it doesnt offer an example that shows the forumla worked out. It does pretty good explanation on what the formula means but even then i do get lost in trying to translate. I was hoping someone could help put some numbers to the formula and sovle and maybe explain a little more, that way I can walk through it on my own and try to figure out how it all works. any help is greatly needed and appreciated. Here is the weblink to the paper http://www.apmaths.uwo.ca/~mdavison/_li ... age.pdfAnd below is the portion I was refering to but the formula doesnt show. I have also added an attachment with the selected formula I would like to figure out. THANKS for any help!!Let us begin by defining the relevant variables and parameters. Let• P = the current price per unit of natural gas.• I = the current amount of working gas inventory.• C = the control variable that represents the amount of gas currently being released from (c > 0) or injected into (c < 0) storage.• Imax = the maximum storage capacity of the facility.• cmax(I) = the maximum deliverability rate, i.e. the maximum rate at which gas can be released from storage as a function of inventory levels.• cmin(I) = the maximum injection rate, i.e. the maximum rate at which gas can be injected into storage (cmin(I) < 0) as a function of inventory levels.• a(I,c) = the amount of gas that is lost given c units of gas are being released from (c > 0) or injected into (c < 0) storage and I units are currently in storage. (When gas is injected into storage fuel is needed to power the injection process, gas can also be lost due to reservoir seepage. The rate of seepage depends on inventory levels.)• T = denotes the time interval of consideration.• E[.] = represents expectation under the risk neutral measure over the random variable P• Ρ= the risk free interest rateWith this representation, our objective is to maximize the expected cash flows of the gas storage facility under the risk adjusted measure. Since the instantaneous cash flow is simply the product of the amount of gas lost, bought or sold i.e. (c - a(c, I)) and the current gas price P, this objective can be written as Subject to In order to solve this optimal control problem we require equations for the dynamics of I and P.The change in I must obey the ordinary differential equation In other words the change in I is simply the negative of the sum of the controlled amount released (c) for sale and the amount lost due to seepage, pumping or any other frictional effects (a). We now require equations for the risk adjusted dynamics of the price process P.

I tried to upload the file so you can see the formula quickly but it wont accept Word or Excel, I am sure it is something I am doing wrong. So if you want to take a look at the link, the formula begins on page six. Otherwise, here is my attempt to show the formula the best way i can within this environment. max E[ e^-pt(c-a(I,c))Pdt] c(P,I,t)subject to c (I)<=c<= cmax(i) min Hope this helps! any guided direction would be super awesome! Latigo