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Money Networks

Learn about discrete-event money models and how to manage your money efficiently with synchronous-reactive money networks. Understand two-way functions, money network properties, and N-way functions. Explore examples, calculations, and functions in managing your finances effectively.

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Money Networks

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  1. Money Networks Manage your money with synchronous-reactive money networks. By Adam Cataldo

  2. Outline • Discrete-Event Money Models • Synchronous Reactive Money Networks • Two-Way Functions • Money Network Properties • N-Way Functions

  3. Discrete-Event Money Models • Transactions happen at discrete points in time, but time, as we know it, is not discretized. • This discrete event model describes this behavior. • This model is accurate but awkward to work with.

  4. DE Savings Account

  5. Present/Future Value problems • An account opened today with $m has present value (PV) $m. • If it is compounded annually at interest rate i, after t years, the account is worth PV(1+i)^t. • I call this amount the future value (FV) after t years.

  6. PV/FV function • Given an interest rate i and a time t, I can calculate PV from FV or FV from PV as follows:

  7. PV/FV function in SR domain • Given the present value, the PV/FV function returns the future value. • Given the future value, the function returns the present value. • For an initial investment of PV left to mature, we use: • f(PV) = PV * (1 + i) ^ t • g(FV) = FV / (1 + i)^t

  8. Specifically

  9. In Ptolemy II

  10. In Ptolemy II

  11. In Ptolemy II

  12. In Ptolemy II

  13. Calculating PV from FV

  14. Two-Way Function • The two-way function is a generalization of the PV/FV function in the SR domain. • The function has two inputs x and y. • Either y = f(x) or x = g(y), depending on which input is known first.

  15. Form of the Two-Way Function

  16. `

  17. Two-Way Function Properties • The two-way function is monotonic. That is, if (a,b)  (c,d) then F(a,b)  F(c,d). • The two-way function is continuous. That is, F(V(a,b)) = V F(a,b) for any chain. • This means F has a least fixed point for any two signals.

  18. Another Two-Way Function • Account with monthly investments m:

  19. Another Two-Way Function • In terms of x, y, f, and g:

  20. In Ptolemy II • This two-way function will not currently run, because the Ptolemy expression language cannot not support the “sum” function. • If it did however...

  21. In Ptolemy II

  22. Money Networks • A money network is any synchronous-reactive network used to calculate monetary values. • A money network describes an investment situation. • This network allows fast redefining of inputs and outputs (present and future values).

  23. N-Way Function • Recall the situation where monthly investments of m are made.

  24. N-Way Function • If we know either m, PV, or FV, we know all three values, because

  25. N-Way Function and

  26. N-Way Function • This suggests a generalization of the Two-Way Function to n signals. • If one signal is known, all other signals equal a function of that signal. • Otherwise, the signals do not change.

  27. Three-Way Function Example

  28. Ptolemy Model(not implemented)

  29. Number of Functions • For the simple three-way function, we require 6 functions. • In general, we require n(n-1) functions for an n-way function. • We can reduce this number to n when all the functions are invertible. This function is one such function.

  30. Key Result: Networks on N-Way Functions • If a set of N-way functions is connected in a graph, knowing the value along exactly one edge determines the values at all other edges of the graph. • This value can be set by another function, such as the constant function in Ptolemy.

  31. Conclusions • Money networks make it possible to determine several present and future values based on a single value. • The same money network can be used to determine different values. • In a connected network, knowing a single value determines all others.

  32. Future Work: Improving Money Networks • Build a library of money network functions. • Improve the GUI representation of money networks in Ptolemy II. • Extend the Ptolemy expression language to handle more general expressions, such as “sum”

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