Dorothy Hartley

Dorothy Rosaman Hartley was an English social historian and author. Daughter of a clergyman, she studied art, which she taught, her interest in history led her into writing. Among her books are six volumes of The Life and Work of the People of England, covering six centuries of English history, she is best known as the author of the book Food in England, which has had a strong influence on many contemporary cooks and food writers. Delia Smith called it "A classic book without a worthy successor – a must for any keen English cook." It combines an historical perspective on its subject with the practical approach of an experienced cook. It has remained in print since its publication in 1954. Hartley was born at Ermysted's Grammar School, Yorkshire, the youngest of three children of the headmaster of the school, the Rev Edward Tomson Hartley and his wife, Amy Lucy, née Eddy. In her 1954 book, Food in England, Hartley gave an autobiographical sketch using the kitchens of her various homes as the background: "My first kitchen was a stone-floored cottage in the Yorkshire dales…Fresh mountain air and the smell of cooking always filled this brightly polished kitchen."

She was educated at a convent of French nuns at Skipton until 1904, she recalled, "the kitchen was alive with stir and bustle, the clatter of clogs and pails, the aroma of breakfast coffee." In 1904, Edward Hartley retired from the headmastership of the school and became rector of a country parish at Rempstone, Nottinghamshire. Dorothy Hartley recalled; the nearest shop was five miles away and we had no car. A butcher called once a week, a grocer once a fortnight. With one maid and a weekly washerwoman it was not an easy house to run."After her secondary education at Loughborough High School Hartley attended Nottingham Art School. During the First World War she worked in a munitions factory. In 1919 she entered the Regent Street Polytechnic in London where she was, according to the Oxford Dictionary of National Biography, a prize pupil, she returned to Nottingham Art School as a teacher in 1920–22. She continued to teach, in London and elsewhere, for many years. While earning her living as an art teacher, Hartley began writing in her spare time.

She sometimes commented on her lack of education, but as The Times noted, "Later achievement suggests she more than made up for it." Many of her books are scholarly in nature, were reviewed favourably by expert critics. Together with Margaret M. Elliot she wrote Life and Work of the People of England, in six volumes, published between 1925 and 1931. In 1930 she published The Old Book, "A Mediaeval Anthology Edited and Illuminated by Dorothy Hartley" with an introduction by Professor George Saintsbury. In 1931 she "collated and edited" the poet Thomas Tusser's Good Points of Husbandry". In 1931 Hartley published what was, until Food in England in 1954, her best-known book, Medieval Costume and Life. In it she showed the clothes of peasants depicted in old manuscripts, with diagrams to show how they were made, photographs of models wearing them, one of the models being Hartley herself. In addition to her skill as an illustrator, Hartley was a keen photographer. In 1931 she travelled by car from Egypt to the Congo, taking many photographs which were exhibited at the Imperial Institute in London.

Between 1932 and 1936 she toured the British Isles by bicycle and car, writing weekly articles for The Daily Sketch. Her topics included horse-ploughing, bread making, clog making, she used material she had gathered during these trips in her books, Here's England, The Countryman's England, Made in England. A tour of a different kind was one she made of Ireland, retracing the steps of the mediaeval prelate Giraldus Cambrensis who had accompanied Prince John there in the twelfth century; this led to her book Irish Holiday, of which one reviewer wrote, "If you want to see Ireland in extreme and unnecessary discomfort, Irish Holiday will tell you how to do this…my only criticism against an enthralling book." Hartley's mother was from Froncysylltau, near Llangollen in north Wales, where the family owned quarries and property. In 1933 Hartley moved to a house in Froncysylltau, it was there that she began work on the book for which she is best known, Food in England, with its chapters on kitchens and fireplaces, poultry, eggs, mediaeval feast and famine, fungi, Elizabethan households, the New World, drying, dairy produce, the Industrial Revolution, "sundry household matters", all written from the viewpoint of an historian and a practical and old-fashioned cook.

On its publication in 1954, the book was received with immediate acclaim, has remained in print since. The Manchester Guardian called it "fascinating…unusually readable"; the Sunday Times, reviewing the seventh edition of the book wrote, "For food scholarship at its best see Dorothy Hartley's robust, irresistible Food in England... As packed with diverse and fascinating information as a Scotch bun with fruit, this untidy bundle of erudition is held together by the writer's huge enjoyment of her subject, her immense curiosity about everything to do with the growth, preparation and eating of food in this country since the Middle Ages." In the post-war years Hartley taught at University College and Goldsmiths' College in London, appeared on tele

Merton's portfolio problem

Merton's portfolio problem is a well known problem in continuous-time finance and in particular intertemporal portfolio choice. An investor must choose how much to consume and must allocate his wealth between stocks and a risk-free asset so as to maximize expected utility; the problem was formulated and solved by Robert C. Merton in 1969 both for finite lifetimes and for the infinite case. Research has continued to extend and generalize the model to include factors like transaction costs and bankruptcy; the investor lives from time 0 to time T. He starts with a known initial wealth W0. At time t he must choose what amount of his wealth to consume, ct, what fraction of wealth to invest in a stock portfolio, πt; the objective is max E where E is the expectation operator, u is a known utility function, ε parameterizes the desired level of bequest, ρ is the subjective discount rate. The wealth evolves according to the stochastic differential equation d W t = d t + W t π t σ d B t where r is the risk-free rate, are the expected return and volatility of the stock market and dBt is the increment of the Wiener process, i.e. the stochastic term of the SDE.

The utility function is of the constant relative risk aversion form: u = x 1 − γ 1 − γ, where γ is a constant which expresses the investor's risk aversion: the higher the gamma, the more reluctance to own stocks. Consumption cannot be negative: ct ≥ 0, while πt is unrestricted. Investment opportunities are assumed constant, r, μ, σ are known and constant, in this version of the model, although Merton allowed them to change in his intertemporal CAPM. Somewhat for an optimal control problem, a closed-form solution exists; the optimal consumption and stock allocation depend on wealth and time as follows: π = μ − r σ 2 γ.. C = { ν − 1 W if T < ∞ and ν ≠ 0 − 1 W if T < ∞ and ν = 0 ν W if T = ∞ where 0 ≤ ϵ ≪ 1 and ν = ( ρ − ( ( μ − r