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However, if the price remains unchanged for several time points, one could close a position at one point and enter the opposite position at another point with the same resulting profit This can still qualify as a reversal system I will not differentiate between these cases This also explains why several maximum profit strategies may exist All of them generate the same profit but different transactions are done at different times, making them unique However, from a purely financial viewpoint, these strategies are not equivalent For instance, a profit obtained from one strategy is realized sooner than the other This profit can be reinvested and result in a larger annualized return This is especially true when trading or investing in more than one market.

t/(RC)

The sphere through the given points is x y (e) For a general conic section the equation is ax 2 so that we get x2 x12 xy x1y1 x2 y2 x3 y3 x4 y4 x5 y5 y2 y12 y22 y32 y42 y52 x bxy cy 2 dx

Notice that in this case we test for two conditions that might cause failure to create the database. If the database already exists, GetLastError() will report ERROR_DUP_NAME. This isn t a problem for us, as it won t prevent us from opening the database by name. If we get a return of ERROR_DISK_FULL we notify the user, clean up, and bail out. If we just want to unconditionally test for success or failure, we could do so like this:

The presence of several markets will further complicate an algorithm for evaluating maximum potential profit when total capital is limited and when transaction costs are taken into account While the properties 1 through 3 may be obvious, property 4 requires a proof In order to prove it, I shall apply the rule of contraries (by discovering the contrary hypothesis) by assuming that a potential profit strategy that consists of more than two transactions is not a true reversal system This means that before the first and after the last transaction, when the strategy is out of the market, there is at least one more interval where the strategy is also out of the market.

Input: Points (xi,yi), i = 1,2, . . . , rn. Returns: *2,1 (x) and *1,1 (x)which can be used to find error values. Initialization: Set C O = z-1 = QO = 0,GIO] = 1, ~ i [ O = -yi, i = 1,2, . . . , m,qioi = 1; t l p! for s = 1 torn If Cs-2 # 0 choose j s E CS-'. Otherwise, choose j , such that D[ '] # 0. Is If no such j , , break. fork = 1 to rn such that k @ Cs-2 U CS-' U Qs-' (may be done in parallel) [ D f ' ] = -G[!-'] Js

(2.35)

The goal is to show that there is a finite number of cases that describe how the strategy can exit an existing position and enter a new one in order to create this added interval in which it is out of the market In each of these cases the strategy leaves a part of the potential profit in the market and cannot be called a potential profit strategy..

with m 2 n, where, following convention, each TOW is a basis vector. Then the lattice is the set A = {EM : 6 E Z"}; that is, integer linear combinations of the basis vectors. Note that a lattice forms a group under addition. It should be obvious that the generator is not unique. Two generator matrices M and A define equivalent lattices if fi = c U M B , where c is a nonzero constant, U is a matrix with integer entries and det( U )= f.1 (that is, U is unimodular) and B is orthogonal, B B = I . Equivalent lattices are essentiallyjust rotated and/or scaled versions of each other.

TOTAL CASH OPEN TOTAL1 CASH1 OPEN1 TOTAL2 1350 1350 0 1350 1350 0 1350 1300 1300 0 1300 1300 0 1300 2800 1300 1500 2800 1300 1500 2750 3900 3900 0 3850 3850 0 4900 4450 4450 0 4950 4950 0 6550 Potential profit = 4450 0 P&L = 2600 Equity = 2700 Cost = 100 P&L/Size = 1 P&L = 500 Equity = 600 Cost = 100 P&L/Size = Reserve 1 = 4950 0 P&L = 2600 Equity = 2700 Cost = 100 P&L/Size = 1 P&L = 1000 Equity = 1200 Cost = 200 P&L/Size = Reserve 2 = 6550 0 P&L = 2600 Equity = 2700 Cost = 100 P&L/Size = 1 P&L = 1100 Equity = 1200 Cost = 100 P&L/Size = 2 P&L = 1500 Equity = 1800 Cost = 300 P&L/Size = CASH2 OPEN2 1350 0 1300 0 1250 1500 4900 0 6550 0