Consider the following stochastic optimization problem: maximize_x, y x + y subj
ID: 3572462 • Letter: C
Question
Consider the following stochastic optimization problem: maximize_x, y x + y subject to x greaterthanorequalto 0.3, y greaterthanorequalto 0.2, 2x + 3y lessthanorequalto 6 P{Ax + OAy lessthanorequalto 1} greaterthanorequalto 0.5. Random parameter A has the same distribution as in question 4. Write a MATLAB program to solve Problem (3). Once you obtained the solution (x*, y*), plot the distribution for Ax* + 0.4y* Based on your answer to item (b) above, check if the chance constraint is satisfied. Remove the chance constraint from Problem (3) and repeated steps (a) to (c).Explanation / Answer
First, let Pine Tree State begin with settled processes. A settled method could be a method wherever, given the place to begin, you'll be able to recognize with certainty the whole mechanical phenomenon. as an example, take into account the subsequent method
x(t)=x(t1)2x(t)=x(t1)2 and x(0)=ax(0)=a, wherever "a" is any number.
Let us say, for the sake of simplicity, time within the higher than process: "t" is barely measured in integers.
So this method goes as follows: a,a2,a4,a8,...a,a2,a4,a8,.... If you recognize the place to begin "a", then you'll recognize remainder of the sequence with none ambiguity. this can be a settled method. in a very settled method, every resultant step is claimed to be celebrated with likelihood one (complete certainty).
Now, let's move to random processes. i'll take Andrei Markov chains as associate degree example to clarify random processes.
My favorite example: Reaching your house of labor from your home. allow us to say there square measure 3 completely different routes do that, all of them equal in distance/traffic congestion/safety. And conjointly allow us to say these routes ran into at numerous points before you reach your workplace. By this I mean, you'll be able to switch between the routes en-route.
Now, as shortly as you get out of your home, you have got 3 selections [A,B,C]. you will decide any of them with likelihood 1/3. Say you decide route A. And at every intersection, you have got additional possibilities: remain route A, switch to route B or switch to route C. you will decide any of the higher than choices consistent with your whim. therefore what happened here? the ultimate route sequence you'll go for reach the workplace (home-->A, A, B, C, A, A, C -->office) isn't "deterministic". during this oversimplified example, your finish purpose (the office) is settled, however your route sequence could be a framework.
Now, however does one apply this to finance? allow us to say the market-price of some portfolio is ten greenbacks nowadays. what is going to or not it's tomorrow? in theory, it will be anything! however I will argue, intuitively, that there's the next likelihood that it's either nine greenbacks or eleven greenbacks and a really low likelihood that it's a hundred greenbacks (unless in fact, this explicit company partnered with google INC. or something). therefore the stock costs square measure a framework (a Markov process, to be precise). Given any explicit stock worth, tomorrow's stock worth is expressed as a likelihood distribution and cannot be celebrated deterministically.