Optimal Dynamic Bidding

1 . A method for determining an optimal bid price for an advertisement in a second price auction, comprising:

dividing an advertisement period into a plurality of time periods;

calculating an optimal bid price for a final time period of the plurality of time periods;

calculating an optimal bid price for each predecessor time period of the plurality of time periods; and

placing a bid for the advertisement using the optimal bid price calculated for a first time period of the plurality of time periods.

2 . The method of claim 1 , further comprising:

calculating an expectation of profit for the final time period; and

calculating an expectation of profit for each predecessor time period of the plurality of time periods.

3 . The method of claim 1 , further comprising:

calculating an expected attribution conversion probability for the final time period; and

calculating an expected attribution conversion probability for each predecessor time period of the plurality of time periods.

4 . The method of claim 1 , further comprising:

calculating an expected cost for the final time period based on the optimal bid price for the final time period; and

calculating an expected cost for each predecessor time period of the plurality of time periods based on the optimal bid price for the corresponding time period.

5 . The method of claim 1 , wherein calculating the optimal bid price at any time period of the plurality of time periods is independent of prior spending.

6 . The method of claim 1 , wherein the optimal bid price depends upon a function that gives a winning rate for an arbitrary bidding price at a given time.

7 . The method of claim 1 , wherein the optimal bid price depends upon a cost function that gives a conditional expectation of bidding cost given winning.

8 . The method of claim 1 , wherein the optimal bid price depends upon a premium function that gives an expectation of bidding profit.

9 . The method of claim 1 , wherein the premium function depends upon the win rate function and the cost function.

10 . The method of claim 1 , wherein the optimal bid price depends upon a conditional conversion probability function with a Markovian evolving state variable.

11 . A non-transitory computer readable medium on which are stored instructions for determining an optimal bid price for an online advertisement in a second price auction, comprising instructions that when executed, program a computer system to:

divide an advertisement period into a plurality of time periods;

calculate an optimal bid price for a final time period of the plurality of time periods;

calculate an optimal bid price for each predecessor time period of the plurality of time periods; and

place a bid for the advertisement using the optimal bid price calculated for a first time period of the plurality of time periods.

12 . The computer readable medium of claim 11 , wherein the instructions further comprise instructions that when executed cause the computer system to:

calculate an expectation of profit for the final time period; and

calculate an expectation of profit for each predecessor time period of the plurality of time periods.

13 . The computer readable medium of claim 11 , wherein the instructions further comprise instructions that when executed cause the computer system to:

calculate an expected attribution conversion probability for the final time period; and

calculate an expected attribution conversion probability for each predecessor time period of the plurality of time periods.

14 . The computer readable medium of claim 11 , wherein the instructions further comprise instructions that when executed cause the computer system to:

calculate an expected cost for the final time period based on the optimal bid price for the final time period; and

calculate an expected cost for each predecessor time period of the plurality of time periods based on the optimal bid price for the corresponding time period.

15 . The computer readable medium of claim 11 , wherein the optimal bid price at any time period of the plurality of time periods is independent of prior spending.

16 . The computer readable medium of claim 11 , wherein the optimal bid price depends upon a function that gives a winning rate for an arbitrary bidding price at a given time.

17 . The computer readable medium of claim 11 , wherein the optimal bid price depends upon a cost function that gives a conditional expectation of bidding cost given winning.

18 . The computer readable medium of claim 11 , wherein the optimal bid price depends upon a premium function that gives an expectation of bidding profit.

19 . The computer readable medium of claim 11 , wherein the premium function depends upon the win rate function and the cost function.

20 . The computer readable medium of claim 11 , wherein the optimal bid price depends upon a conditional conversion probability function with a Markovian evolving state variable.