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Hand-Outs, I

Hand-Outs, I. Graded Course Works #2 (brown folder.) Nice work; more comments on Thursday. Course Work #3. Due (next) Thursday November 25 (green.) Student surveys; yellow. Fill out and give to me or Maths Taught Student Office. Attendence sheet (just the one.). Hand-Outs, II.

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Hand-Outs, I

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  1. Hand-Outs, I • Graded Course Works #2 (brown folder.) Nice work; more comments on Thursday. • Course Work #3. Due (next) Thursday November 25 (green.) • Student surveys; yellow. Fill out and give to me or Maths Taught Student Office. • Attendence sheet (just the one.) MATH 2510: Fin. Math. 2

  2. Hand-Outs, II • Updated course plan (blue as usual.) • Exercises for Thursday Nov. 17 Workshops. (Qs and As.) • Commented table of the normal distribution. • These slides. • A few spares of CT1, Unit 14 w/ comments. • Many spares of last week’s Workshop sol’ns. MATH 2510: Fin. Math. 2

  3. CT1 Unit 14: Stochastic rates of return Rate of return each period, it, is stochastic (or: random.) Returns are independent (actually not the worst assumption ever made.) We invest over the horizon 0 to n. What can we say about our time-n wealth? (Expected value, standard deviation, moments, distribution, …) MATH 2510: Fin. Math. 2

  4. A single (£1) investment The central point of attack is the equation By raising it to powers (1 and 2 mostly; 3 and 4 in CW #3) and taking expectations we arrive at equations for moments in terms of it-moments. (Nice w/ iid, manageble even if not.) MATH 2510: Fin. Math. 2

  5. (£1) Annuity investment The central point of attack is the equation By raising it to powers (1 and 2 in particular) and taking expectations we arrive at recursive equations for moments. MATH 2510: Fin. Math. 2

  6. Annuities w/ the iid returns In case of identically distributed returns we get with j = E(i) and v =´1/(1+j). MATH 2510: Fin. Math. 2

  7. 2nd moment of annuity wealth For the second moment we get This is easy the implement in e.g. Excel. (Go to file w/ Table 1.3.1.) (For non-identical i-distributions just put time-indices on j and s.) MATH 2510: Fin. Math. 2

  8. Log-normal returns Another often used, none-too-bad assumption is A sum of independent, normally distributed random variables is itself normally distributed, and the central point of attack is MATH 2510: Fin. Math. 2

  9. For single investment we can (when equipped w/ a table of the normal distribution function) find probabilities (for e.g. shortfall or outperformance) easily. A fact: For annuities the (log)normality assumption doesn’t really help much. MATH 2510: Fin. Math. 2

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